milimelo

You cannot restart where you left off. That green card eligibility ended when you left the US 5 years ago. Even if the GC was issued it would only have had a 2 year duration at which point you would have had file for removal of conditions. That time passed a few years ago.
Sorry to say, but you have no claim to residency at this point.

If they don't intend to be living in the USA its kind of silly to renew/apply for a new green card, its not a visitor pass to the USA. The green card is for LIVING in the USA.
The green card status becomes abandoned after not living in the USA for a year. I'm pretty sure their GC status was canceled before the card expired.
If they want to visit they should apply for a visitor visa.
If they want to live in the USA they will have to be sponsored and start all over again with the paperwork and fees and wait till approvals etc.

What is Hold Departure Order? Does this mean the Philipines government stopped you from leaving their country for the last 6 years and if so why?
You most likely will not be let into the USA, as you'll be considered to have abandoned residency with such a long absence. You will need to be petitioned again, via a I-130 as you say. It will not be any faster because you were an lpr previously. How long it takes will depend on who petitions for you.

Important: Show up anyway at the original time on the original day, with your original appointment letter in hand.
If they won't let you in, you can say that you never got a letter to the contrary.
If they do let you in, you're where you were to begin with.
If the history of other VJ members is to be believed, it can be folly to believe these "cancellation" letters.

Do an immediate debriefing with your husband. Ask him to write down every question he can remember and every answer he gave--this is not the time to be defensive, but rather to put yourself in the place of the CO and see how you would have reacted to his answers. Also, what other red flags are there with your case--a few bad answers usually aren't enough to derail a case. Be brutally honest with yourself--and do it immediately while everything is fresh in his mind.
Then come back and tell us all the red flags as well as the questions and his answers, and then we can start to help.

Visiting the US and living in the US are worlds apart.

Well she can either wait for ROC and change her GC then, OR she can pay the $455 fee to file the I-90 to replace the greencard with the married name.
She shouldn't change anything until her GC is changed. When working she works in her GC name, which means she'll file taxes in that name, but it needs to match her SSN. And you can't change the drivers licence until she changes the SSN.
It's just simpler to do the GC first THEN do the rest. She can of course call herself by your last name, but any legal forms she is maiden name, until she changes the GC.

May be time to get your spouse's representative involved as it has been over 6 months and no AOS GC.

I have read here stories where people got a 10 year card by mistake and then were deported in absentia when they failed to remove conditions after 2 years.
OP - If you are approved on your interview date, you will get a 2-year card which is good for 2 years after your interview date. Yes, you will file for removal of conditions when you are nearing your 4th wedding anniversary.

That penny's worth of advice applies not only to what you should have done, but also to what you still should do. Forget everything that's gone wrong up until now. Go back to square one, get it right, and start the process from the beginning. Yes, the process is complicated, but it's not so complicated that you need an attorney. Anyone with average intelligence and a willingness to learn can handle a routine case on their own, and your case seems pretty routine.
Now, if you'll permit, I'll add a few comments to your bullet list...
(a) conduct the marriage in the country you intend to take residence permission.
Not always possible. Getting married in the US is a snap in most states. Getting into the US in order to marry here is considerably more difficult. You've spent some time in East and Southeast Asia, so you probably know that getting a visitor's visa in some of those countries borders on the impossible.
The percentage odds of my wife or any of her family getting a visa to visit the US could be counted on the hands of Three Finger Jack. On the other hand, getting married in her country is a bureaucratic nightmare which includes an interview by the VN government wherein she has to prove she's proficient in MY language by translating questions and responses in front of two professional translators. Even with her current level of "Vinglish" proficiency, which I understand completely, she couldn't pass that test today. For us, the only practical option was a K1, which also came with the added bonus that her older teenage kids would be eligible for K2 visas, while they wouldn't have been eligible for CR2's. How did I learn this stuff? Basic research.
(b) expect confusion between the two different country agency when explaining your condition.
I'll take this a step further. NEVER ask a low-level government bureaucrat for help with a complicated bureaucratic process. The first line of "defense" that any agency of any government puts up between them and the citizens they serve are low-paid uneducated dolts who would only intentionally help you if they did it accidentally. If they actually knew anything about laws and policies then they'd have a better job deeper in the bureaucratic machine, and farther from the customers. Do your own research. Most lawyers are no smarter than you, and you are equally capable of understanding laws and policies. In the 21st century you also have a wealth of educated people on the internet you can turn to for help. Proceed only when you're sure that YOU understand what to do.
(c ) remembering Governments are not logical, the systems are made complicated, and if someone tells you otherwise they are full of fluff. ( But rummer has it that Immigration Reform is on the way. . . just don't hold your breath.
For every seemingly pointless bureaucratic hurdle they throw in your way, there is a valid and sensible reason if you dig deep enough. Let's look at the marriage certificate thing as an example...
Immigration fraud has always been a big problem in the US, and probably always will be. This is understandable, given that the US is the biggest immigration magnet in the world, beating the #2 country by a factor of six. Bear in mind that this is based on a perception of the US that doesn't really jive with reality, and there are other countries where the standard of living is actually much better (Switzerland, for example). Nevertheless, more people have a desire to immigrate to the US than anywhere else.
Many people's eligibility to immigrate is based on family relationships with US citizens and LPR's. The proof of their eligibility often hinges on foreign documents like birth and marriage certificates. Before there was a standardized method for verifying these documents, US immigration authorities were frequently defrauded by aliens presenting forged or otherwise fraudulent documents. Congress decided that the responsibility for establishing uniform standards would fall on the Department of State, since they are the only government agency with an official presence in each of these foreign countries through the US embassies and consulates. The end result was a collection of standards called the "Fee and Reciprocity Tables", which details for each country whether a particular type of document is available, who it's available from, and what exactly a document should have in order for it to be considered valid. For all US government agencies that have to deal with foreign documents, the reciprocity tables are the "bible" they rely on.
An inference you may freely draw from the above is that the average US immigration officer wouldn't have a clue if a document were valid without the reciprocity tables, as well as visual examples of valid documents. You could have a perfectly valid document which would be accepted by a foreign government without question, but if it doesn't exactly conform to the reciprocity tables then the US government won't accept it. Armed in advance with this knowledge, you know what you need to get in order to satisfy them.
As far as immigration reform, as you say, don't hold your breath. I don't think it will be coming soon. If it does, it won't make immigration easier. In any country with a weak economy, the public mood will always be anti-immigration. Most Americans don't want to see immigration made easier, and they want much stronger enforcement of illegal immigration laws.

You are limiting your options to what is convenient for you. Appealing the fiance visa process may not even be an option. Usually they just notifiy you the petition approval has expired and you can try again if you wish. Even on appeal, the same issues will be there. The strongest evidence of a bona fide relationship is time spent together in person. In your situation, my opinion is that you'll be wasting your time trying anything until you can spend some significant time together as a married couple. Consular officers don't care one bit about the inconvenience to you. Bona fide relationships with foreigners are seldom convenient. Everybody here knows that first hand.

Many states (maybe most) have mandatory arrest laws for domestic violence. If someone calls the police and claims they were abused, and the police see any evidence of physical abuse - scratches, bruises, etc., then they are compelled to make an arrest. If she is ever alone with him then he can smack himself around and call the police and blame it on her. If he knows she's alone, even if she's not with him, then he can do the same and she won't have an alibi. This is a serious risk, and if he's getting guidance from people who understand the law then they'll be able to tell him how to pull it off. There are web sites that specifically instruct immigrants how to do this.
She needs to lawyer up, and she needs to make sure she's never alone.

Its sponsoring a foreign national that compromises it.
It does cause problems even for military people. They have to retest and take frequent testing/polygraphs to prove they are not giving info to this foreign national etc.

Sou--you gotta face the facts--you are in a mess, and while we are all trying to help, we also make fun of ourselves--and you--sometimes. Heck, I'd live in Canada in a heartbeat if I could, but I can't--take it as both a VERY SERIOUS option as well as lighthearted. I have to say that if I were the CO and you dealt with me even a little bit like you deal with us on this website, I would NEVER approve you to move to the US, or to visit either. You are a jerk here, and probably there, and maybe in all aspects of your life. Do you not get it?? We are pretty laid back in the US, but do not suffer fools lightly, and you are acting like a fool. If you just can't help it, you are doomed to NEVER live in the US, so think about other options--ever asked your wife about Canada?? Didn't think so !!

Being a relative of a US citizen is the ONLY basis on which a VWP entrant can adjust status. That's why VWP entrants are listed in the category of people who cannot apply for adjustment of status, and being an immediate relative of a US citizen is given as an exception. Be very careful trying to extract an understanding of immigration law from the form instructions. There are a great many people who thought everything they needed to know was contained in the form instructions, and immigration attorneys make very good money trying to help these people out of the mess they make for themselves.
Adjustment of status after entering with any sort of non-immigrant visa or entry pass is an exception to normal immigrant visa processing, and not just an alternative to it. It is meant to be used in unusual circumstances where it would be impossible for someone to return to their home country for immigrant visa processing, or where someone's circumstances had changed substantially since arriving in the US and it would be needlessly bureaucratic to force them to return to their home country for immigrant visa processing. What you're talking about is planning this in advance as if it were some sort of easy shortcut around the normal immigrant visa process. This is called "preconceived intent", and it's illegal. USCIS can't read your mind and determine what your intentions were when you entered the US, so it's the job of the US consulates abroad and the CBP officers who work at the immigration desks at the ports of entry to try to detect people with preconceived intent and stop them.
You are now the spouse of a US citizen. You may be asked about your marital status when you enter the US. If you tell the truth then the CBP officer may refuse to admit you to the US because they consider you a risk for preconceived intent to adjust status. Alternatively, they may ask you if you intend to adjust status. If you say "no", and subsequently submit an AOS application, then your AOS application will be denied, and you'll be barred from returning to the US for material misrepresentation.
If you'd like to test your theory about intent not being an issue then I suggest you arrive in the US using the VWP and tell the CBP officer that you intend to adjust status based on your marriage to a US citizen. I guarantee you will be denied entry.
As a VWP entrant, you are required to give up any right to appeal any decision by any US immigration officer. If you are denied entry to the US then you will not be able to use the VWP again. If you are denied AOS then you will be immediately removed from the United States - there will be no deportation process, and no hearing in front of an immigration judge. Any decision by any US immigration officer is final - no review, and no appeal.
If you intend to immigrate to the United States then follow the proper and legal process, and obtain a spousal immigrant visa. You'll avoid a lot of potential headaches, you'll get your green card soon after arriving in the US, and it's cheaper!

You're not work authorized - nothing to contest. You are not allowed to work without EAD or appropriate work visa - H1B...

If you want those immigrant visas you WILL get the US embassy what they require from you. All medicals and police records expire after 12 months, need to get the new ones done. And yes, the cost is on the immigrant. So count your lucky stars you have a qualifying US relative to sponsor you as there are millions of people who would consider themselves lucky to get into the US so easy.

After 13 months you are pissed off that they are proceeding with your case? Why? Because you need another medical and police certificate?

Being strict does not mean more visa fraud – if they are not strict then anyone and everyone would be in US….lol
If ppl stop mis-using their visa when they are granted and return back to their home country then CO’s would not be strict.
PPl enter on tourist visa just to give birth in US, ppl enter as student or tourist and file for AOS coz they feel they are so special and count not wait for 8-9 months without their spouse.
PPL enter on tourist and student visa all the time to find work in US, ppl bring their parents under pretext of tourist and parents never return back to home country and on and on.
Also it depends on the economy situation of the applicants country and political relation between US and the country.
With all these happening how do you expect CO to welcome everyone with open arm who are applying for visa?

No one here is going to encourage you to try and 'bypass' US immigration and 'sneak' back in through Canada. First, it is a violation of the terms of service for this site to support or offer any advice about fraudulent immigration practices. Second, as a Canadian who regularly traveled back and forth between the US and Canada I can guarantee you will not find it 'easier' to enter the US from Canada.
When you arrive at the border US immigration will enter the train. They will ask to see your green card. They will ask you how long you were out of the US. They will check your answer against their records electronically. If you say anything differently than the truth, then you will be removed from the train and the train will continue without you while they go through your file more carefully. If they determine that you lied to them then they may just deny you entry if you are lucky. When they realize you have been out of the US for 3 years they will question you carefully. Your answers will determine whether you are just denied entry or if you are charged with misrepresentation and immigration fraud. Discrepancies in the passport you use may or may not add additional red flags and raise further questions. If you are anything less than truthful then you risk a lifetime ban upon ever returning to the US. If you are truthful, then you may well be denied entry because you abandoned your permanent resident status - unless, as Jim vaPhuong pointed out, you can offer overwhelming evidence that your absence was beyond your control. That will also only work if you had a 10 year card. If you had a 2 year card then it expired well over a year ago and cannot now be renewed.
You are best advised to go to the US Consulate and see if they will issue a returning resident's permit or not. Your next alternative is to arrange your transatlantic flight through Dublin that has a pre-screening for US immigration so that if you are denied entry you will be able to get your fare back (with a refundable ticket). If you arrive in the US and they deny you entry there then you will be put back on the next flight out - at your expense.
US immigration is nothing to fool around with.

Sorry, but I disagree with this. You have made conflicting statements about emailing the school. Talking to the school. Waiting for them to get back in touch with you. If you had talked to them, you would know if they were DHS approved or not. If you had talked to them, you would know the requirements for admission and answered my questions about what tests you had taking (GRE, ACT.. etc....)
If you have been in contact with them you would not be asking questions like this one.
Your inability to either get your facts straight or keep up with what you have already said looks extremely suspicious.
The bottom line is that you are not going to meet the requirements for admission into a DHS approved institution here in the US.
Your grades are not good enough. At best, your grades may get you into a vocational school. I haven't seen many of those approved by the DHS. You have not taken any exam for admission into college. I don't care if you are from Montana or China or India, much less the UK.... You MUST take these exams. By the way, India kicks our butt with the math SAT scores. The fact that you have no idea about what I have already expressed to you in terms of college admission proves that you have NOT looked into it sufficiently. You are fishing for a way to get over here and be with your BF. Plain and Simple.
This is exactly why the laws are stringent to catch little things like this. As I previously have posted. Just go for the K1 Visa. But it sounds like there is a little problem of money. You have already been "stranded here because you missed a flight and had to wait for your BF to work and make the money for the ticket back home". Which subsequently caused you to overstay.
You have a lot of obstacles to overcome. You also said your BF was coming over there to finish school? Maybe that is a much better plan.
There is no SIMPLE way to get through this and USCIS is trained to spot such ill advised attempts as yours should you even get to the point where you are able to apply for a student visa.
If you want to be with your BF. Then he needs to get a job that can support him and you, file for either K1 or IR1/CR1 (should you want to get married before then) and come over here legally. Marriage is a huge HUGE responsibility.
This is not taking a car out for a test drive and see if I like it scenario. There are long term requirements for bringing a foreign spouse or fiance to the US for good reasons.
Keep in mind that if you are denied by the USCIS because of reasons thought to be a fraudulent attempt to gain entry into the country, that you may be banned from entering the US... Possibly forever.
Think very carefully before you say or do anything else that may or may not incriminate you further.

Be careful basing your decision on the anecdotal experience of anonymous people who post on the internet (including me). Some of the people who said that "nothing happened" may be lying to you. Unless you left the US back in the digital stone age, odds are pretty good that DHS knows when you left the US, and when you try to reenter they'll know how long you've been gone. As Bob mentioned, if you had a conditional green card then it wouldn't matter when or if you left the US - not applying to remove conditions would automatically result in your green card being cancelled.
Sounds like you've got three options:
1. Buy and ticket and take your chances. They might let you in without any questions (odds are slim, in my opinion). They might deny you entry, turn you around, and put you on a plane back to France (odds are high, in my opinion). They might parole you into the US so you can make an appeal to an immigration judge (odds are remote, in my opinion).
2. Try to get a returning resident visa from a US consulate. You'll need to prove that the reason you stayed abroad more than a year was unforeseen, and beyond your control. They're required to consider the length of time you've been outside the US when weighing the validity of your reasons. For three years you'd practically need something like you were kidnapped by the French Mafia and held for ransom, and just recently managed to escape.
3. Stay in France.
Of the three options, only #3 has a 100% chance of success.

Actually it does matter... If they had a 2 yr conditional GC then there's a chance that they were deported in absentia since they obviously didn't file to remove conditions!

To heck with business licenses. Simply tax the living ####### out of them, to the point of bankruptcy, for hiring illegals
Who could be against a law that punishes employers for exploiting humans and failing to comply with laws designed to provide a basic level of income and safety for all workers? Anyone? Someone?
Amazing that among ALL the politicians, NO ONE has even suggested a law that everyone agrees with. Kinda makes you think they really don't want to fix the "problem".

Just a small correction. It will be a Consular Immigrant Visa Unit abroad that starts corresponding with the foreign fiancee, not USCIS. Informing the visa unit you will not be applying for a visa, is what will avoid any problems with your ability to continue to use your current visa.