Brother Hesekiel

Your wife filed for divorce in absentia. It doesn't really matter if she served you or not, 'cause based on the duration of your marriage and the fact that she will state suspected fraud as a reason to dissolve the marriage it will be a smooth ride all theway. You can claim all kinds of stuff, but in the end you'll be going home. My advise to you: accept that your marriage didn't work out, and go home without much fuss. Wisdom is knowing when you can't win a fight, and cut your losses. It's really that simple.

Having a child is proof of insufficient birth control. It can be a token of love . . . or an accident. There's no general yes or no answer to your question.
If you are a in loving relationship, the child is just the icing on the cake. If you file your I-751 with a waiver, because the marriage went downhill fast and you got divorced, the child is not going to make much of a difference.
So, yes, RoC can be denied even if the couple has a child together, but it will only be denied, if the USCIS feels that something is not kosher, and has . . . um . . . evidence to that fact.

I guess if I was a criminal, the logical thing would be is to make a real gun look like a toy gun so cops don't shoot me.

HI
no, because you will be filing for citizenship under the 5 year rule and not through marriage
they might ask you about your marriage at the interview, but since you have a divorce decree, that's about it. you don't have to prove that your marriage was bona fide, that's under the 3 year rule

LPRs of any nationality require only their green card and valid foreign passport to visit Canada or Mexico; this is because of special treaty provisions.

No,
none of that is possible.
Your wife's residency was deemed abandoned in 2002, after she'd been outside the US for a year. It rendered her Green Card invalid after the fact and it cannot be resurrected. She'd have to qualify for immigration once again on her own merits.
In addition know that entering the United States on a non-immigrant visa (or in case of the UK, as a visitor under the VWP) and the intent to immigrate is a felony and could get her barred for life.
You'll have to file and I-130 petition in her behalf and . . . voila . . . about 12 months later the good people in the US consulate in London will interview her and issue her an immigrant visa afterward.

If your wife leaves the US without AP, AoS is considered abandoned by default and she'll need a CR-1/IR-1 in order to return. Takes about a year.
She won't get a B2 again because she has immigrant intent. That aside, entering the US with a non-immigrant visa and the intent to adjust status is a felony and would get her barred from the US for life. It's one thing to get married on a vacation "out of the blue" and then, surprise!, wanting to stay, but leaving as a married woman and returning as a tourist and then trying to adjust is immigration suicide and an easy feather on the hat of an I.O.
I'd try to get emergency AP. If that doesn't work, and your wife is not a world-renown neuro surgeon needed to save her parent's life, I'd postpone that trip. Life is all about choices, and here you guys have a choice.

No,
none of that is possible.
Your wife's residency was deemed abandoned in 2002, after she'd been outside the US for a year. It rendered her Green Card invalid after the fact and it cannot be resurrected. She'd have to qualify for immigration once again on her own merits.
In addition know that entering the United States on a non-immigrant visa (or in case of the UK, as a visitor under the VWP) and the intent to immigrate is a felony and could get her barred for life.
You'll have to file and I-130 petition in her behalf and . . . voila . . . about 12 months later the good people in the US consulate in London will interview her and issue her an immigrant visa afterward.

If your wife leaves the US without AP, AoS is considered abandoned by default and she'll need a CR-1/IR-1 in order to return. Takes about a year.
She won't get a B2 again because she has immigrant intent. That aside, entering the US with a non-immigrant visa and the intent to adjust status is a felony and would get her barred from the US for life. It's one thing to get married on a vacation "out of the blue" and then, surprise!, wanting to stay, but leaving as a married woman and returning as a tourist and then trying to adjust is immigration suicide and an easy feather on the hat of an I.O.
I'd try to get emergency AP. If that doesn't work, and your wife is not a world-renown neuro surgeon needed to save her parent's life, I'd postpone that trip. Life is all about choices, and here you guys have a choice.

Improving legal immigration is at the bottom of the pile it won't win enough votes and like pretty much all politicians all Obama cares about is votes. Shame as it would be a lot easier to fix than illegal immigration!

The reentry permit only prevents a Green Card holder from losing her residency automatically when being out of the country for a year or longer. Once she returns, she'll have to prove that she did not abandon her US residency. However, the US residency is automatically abandoned when a Green Card holder establishes or re-establishes residency outside the US. If Dutchiee moves back the Holland she'll establish residency there. That would be the end of it, reentry permit or not.
Dutchiee, unless you absolutley have to, I suggest you ride the train for 3 years until you can become a US citizen. At that time you can come and go as you please.

It is more likely you were refused because the visa officer could not see you had any reason to return to Libya after you completed your studies and/or doubted your financial resources to pay for the course of study.

He just made the job of securing the border even more difficult by doing what he did. Rightly or wrongly, this sends the message that if you come here, you'll get legal status down the road. The same thing that happened when DACA was instituted. 1000s of unaccompanied minors showed up at the border.

Luckily for you and all of us, the US is not a prison, so if you want to introduce your wife to your family, you have a right to do that. I don't know if that's reasonable, but I know that it is legal. Life is all about choices and that's part of what makes life so interesting.

No, they do not take your Green Card away. Your Green Card has your photo on it and a magnetic code and lots of information about you, and the NOA1 has none of that. The Green Card extends the validity of the Green Card and both go hand in hand and thus belong together.
You will not be able to get an I-551 stamp in your passport, simply because you have a valid I-551: your Green Card, now extended for another year.

Your post proves nothing other than refute a claim by someone else's false claim. If you read factcheck.org carefully it confirms that yes BILLIONS are spent on illegals, just correcting the grossly inflated numbers of the false claim.
Illegals cost the US Taxpayer BILLIONS. FACT.
Focus on the actualities of US Policy. We have over 11 million illegals here in the USA. They are here ILLEGALLY circumventing entry requirements and immigration law. They utilize health resources and welfare resources. FACT. Many of these folks are here and working hard. That's great, but they are here illegally and taking jobs from US Citizens. They are making money here and mostly not paying taxes. It doesn't mean they are bad people. I live in one of the highest percentage of illegal alien counties in the USA. Many lovely people. However, there are many many illegals who are criminals, cheats, scammers, and scumbags from around the world who should be sent home because they are breaking immigration laws and cheating the system. And I am sorry, that includes includes illegal parents in my opinion. Even if they are rocket scientists but here illegally they need to go home.

Roki,
there are two ways to file for RoC:
1) happily married, living under one roof
2) divorced.
If you read this, twice, you'll see that you are neither 1 nor 2 right now. You are in the twighlightzone as you are not happily married any longer and thinking about divorce, and you are not divorced either. Admittedly, you are closer to 1 than to 2, and you could successfully argue that you are still be counted under 1, but it's a close call.
Depending on what state you live in, your divorce can take a few weeks or over a year. Find that out first.
Best case scenario would be that you notify USCIS that you wish to apply with a waiver since you are planing to file for divorce. If you can get this done quickly, it will only throw you back a few weeks or couple of months.
Worst case scenario is that it will take a year for you to get your divorce finalized. If you convert your RoC petition to a singular filed one with a waiver, you'll eventually (roughly 3 months from the time you start this) get an RFE where they ask for your divorce decree. Well, since you don't have one and can't get one for another 9 months, a few months later the USCIS system automatically will seek to get rid of you. You'll receive a letter and will have a date with an immigration judge, at which time your attorney will tell the judge what's happenin' and ask him to put the proceedings on halt 'til your divorce has been finalized and you have the decree in hand. In almost all cases the judge will sign off on this.
Once your divorce is finalized, you submit the divorce decree and USCIS can adjudicate your RoC petition.
You can become a US citizen by means of naturalization as early as the day you have become a resident, just 5 years later. At the 5-year mark your marital status becomes irrelvant.
Now . . . assuming you are rolling the dice and do nothing, and you not only get divorced before your RoC has been adjudicated, but FILE for divorce while your I-751 is pending, you are setting yourself up for serious problems at the N-400 stage. Even if you file after 5 or 6 years, the I.O. will have a look at your divorce decree, and guess what . . . if he finds out that you filed for divorce while your RoC petition implied that you were still happily married (see 1), he'll interpret this as fraud, and I don't have to tell you what that could do to your American dream.
So right now you are at a cross roads, and which way you decide to take, it's going to suck big time. The very first thing you need to find out before you do anything is how long it would take in your state to get a divorce done. Only then you can decide if you want to roll the dice and be the nicest spouse the world has ever seen for a bit longer.

You can't find out because you weren't the petitioner. Since you know they suspected you of a sham marriage be prepared to prove this one is a bonafide relationship. That's all you can do.

Mixed feelings about what part? Him being there illegally will have no effect on you. You are on the hook for the I-134, but that'll expire when his I-94 does (90 days after he enters).
If you don't want to marry him and you've been 100% clear to him about this, he shouldn't want to come to the USA anymore to be with you. Make sure you are clear with him. After that, if he wants to be an illegal immigrant, well, that's his problem not yours, but why would you think he would do that?

Ahhhh.. So we have moved to the "do I have a case against him" stage... Interesting... To answer your question, probably no as there is not "demonstratable" proof of actual abuse... You are not locked in, you are not being denied food and shelter and there is no physical abuse... proof Such as police report, fear for your life or actual endangerment... Is he a jerk, yes, but filing a claim based on this would I believe, be unsuccessful... Sorry your journey to America ended like this.

Looks to me you're better off going back home. Divorce him and move on with your life. You deserve to be happy.

You have been detained for shoplifting, charged with petty theft and paid the fine. You did not do that because you were accused mistakenly, but because you were guilty as charged. You are a thief.
Yet you did not disclose this, wrongfully assuming the Feds are too stupid to find out within a comprehensive FBI background test.
Tell you what: if I had been the I.O. I would have seen this as a deliberate misrepresentation and declared you a persona non grata for the rest of your natural life. If I were you, I would thank my god for sparing me deportation and keep my mouth shut for another 3 years. If I was the judge getting your complaint on my table, I would order you deported before going to the bathroom.
You apparently have no idea how lucky you got.

My daughter and her husband traveled from Europe to Maui, Hawaii, on a B2 with the express intent to get married and to spend their honeymoon there. It was great (I love Maui), and there was absolutely nothing illegal or even secretive about it as we had this planed months before with hotel reservations and all.
It's called tourism, the source of much revenue for Uncle Sam.

Where I come from, and, yes, it's been a while, Travel Health Insurance cost about $11 annually, and covers absolutely everything short of a ####### job. No tourist in their right mind would travel to a foreign continent without it, and if a knocked-up woman ready to pop does this, it cannot be explained by reason alone.

I personally agree with your parents. You are too young to get married.
A guy in his 20s is just at the start of getting his fill of excitement. He is ruled in large part by his lower brain and hormones and needs to have fun in life before he can slow down and get married. If you deny yourself this utmost important phase of life, you eventually will want to catch up on it, which is why close to 80% of all marriages between 18 and 25 in the United States are doomed to fail and end up in divorce. That's a fact.
But I also feel that you are old enough to make your own decisions and mistakes, and while you should be respectful to your parents and soak in their input, by no means should you accept everything they say just because they say it.