Just Paul

Yes it is a real American thing.

Adoption terminates the biological parents rights with very very few exceptions.  I would be very surprised if USCIS would recognize them as your "parents".  Hopefully someone has something else to say about this.  Probably a case for an immigration attorney.

You should get a message from the consulate normally a few weeks after they receive it.   

If the CO asks "do you have a boyfriend" the J-1 will not be issued.   

There is a question on the I-129F about being a previous beneficiary.  Just answer it and be aware the interviewer will probably ask about it.  It likely happens more than we think it does. 
 
Best of luck to her.

The pretty much ask about how you met,  marriage, what USC does for work and where you live.   Just take your time and answer truthfully.  If you don't  understand something just ask.

Please update you timeline to make it easier for us to help you.

What visa was denied?  A B-1 or L-1 or H Series.    What is your citizenship?   If you are Australian you might still qualify for ESTA if the company was denied a L-1.  If it was a L-1 and you had the embassy deny you, at or after an interview, then you won't be able to apply for ESTA for a while.   Regardless applying for the ESTA doesn't cost that much.

Just remember that the medical is good for 6 months and that is the last date for you to enter the US. Sometimes folks forget that and it becomes an issue of the Embassy needs some more documents or clarification.

By the time you adjust status and get your cards the K1 line is longer.   Plus it costs more.  Many on here will say that the CR1 is the best way to go.  While I agree 1000%, each case is different.

You will pay US income taxes  on your worldwide income.   If you lease or rent out your house to others that is income. Dual citizenship does not matter.  You can receive a credit for the income taxes you pay in the Philippines.    
 
What visa did you obtain your green card with? Is it 2 year or 10 year?  If you are on a CR1 you need to spend more than half of that 2 years in the US , with less than 6 months gone at a time, if you intend to file for Removal of Conditions and you will need to show you filed US taxes.

It took us 6 weeks to get an appointment in Mexico.  It varies by Embassy / Consulate.  I know it is hard to wait.  We all have had to wait.  

Your best opportunity is the getting married and filing the CR1 visa.  Like it has been pointed out K1 visa are hard to get.  Just compare the numbers in the reports.
 
CR1 does take longer but is has better success and is cheaper in fees. If it gets denied you can appeal.  Plus you don't have to wait for a green card and you can travel right away. 

Congrats!! This is great news!

My wife was interviewed this week in Juarez Mexico for CR-1/IR-1.  She was in the waiting area for almost two hours. She said she only heard two denials and probably a dozen that got blue sheets requesting for more information.  Usually out of date police reports or missing documents.   She was given one also asking me to come back with here the same day as they had some questions on our total package.  She was approved.
 
Everyone else got approvals.  And most of the interviews were very short.

You don't make reservations until you have an interview date set.
 
Trip cancellation insurance doesn't usually cover this type of change.
 
If you can't change the trip just go out and have a good vacation and grab some more evidence of the relationship.

If you have a CR-1 or IR-1 Visa you can literally leave the US the same day you arrive.  I have seen this many times from Mexico in a similar situation as the OP.   There should be an annotation that says the endorsement functions as an I-551 for 1 year.
 
You do not need to wait for your Green Card.  Your Visa will function as a 1 year GC/EAD. 

You can have dual residence.  You can even get it started in the US.  https://texmexexpats.com/mexico-visa-process-part-1/
 
The minimum you need for DCF is a Temporary Resident Card.  If you have a business in Mexico you shouldn't have been traveling on a tourist visa.
 
We got married in Hong Kong and at the consulate there it took 5 hours for my wife to get her permanent resident entry visa.  In Sonora then it took a few week to get her green card.
 
You can still try for his tourist visa or get married and have him able to come via DCF within 3 to 6 of filing.
 
Note that the CR1 is an immigrant visa and he has to have plans to immigrate. Basically more than half of the first 2 years needs be spent in the US. I agree that the B1/B2 seems like a better fit but he has to show ties to Mexico and that can be hard to do.
 

The  denied K1 won't have any effect on your spousal visa.  It is just like starting over.

I think at least 4 hours is best.  Depending on how busy they are it might just take an hour but it is better to be safe and get the most time between flights.  My recollection is that she has to go thru secondary inspection the first time.
 
What POE are you arriving at?

That is our timeline. Not an expedite.  We did do a DCF in Juarez as we were blessed in that I have permanent residency in Mexico and that she obtained her Mexican Residency in about 5 hours (well there was a bit of drama the first time we tried). Our first consulate appointment date was December 27th.  Within two weeks, after checking 3 or 4 times a day, I was able to get a September appointment. Next Monday is her medical and Tuesday for her consulate appointment.
 
Good luck on your journey. 

Sorry for the late reply.  When my wife left the Philippines from Manila she didn't have to pay the travel tax.  They said as long as she had her CFO stamp and  immigrant visa she was exempt.

Just to point out that lawful residency is not the same as citizenship.  You can easily file when he has residency.  If you are waiting for him to be an Italian Citizen you will wait much longer.  There might be an issue where his passport expires during the process.  If so hopefully he can renew it in Italy.
 
I would recommend that  you check with the US embassy  / USCIS in Italy to see if they will allow his asylum residency status to be used as residency for the application or if he has to have "permanent" residency.  Again you might have a timing issue with his passport expiration.  In any case you will be applying via the lockbox in the US.

Research K1/CR1 denials visa more.  In the past, prior to the new policy implementation of Sept 11, 2018,  you can appeal a I-130 decision and not a I-129F.  The CR1 might take longer but it is definitely faster then having to refile the K1. The CR1 is also cheaper and has other benefits. In any case a Tourist Visa is probably not going to happen.
 
We wish you the best in the  process.
~Paul

My Filipina wife and I found it was easier and quicker and actually cheaper to marry in Hong Kong this past March.  We sent in the marriage paperwork 2 weeks before and spent about 5 days in HK for the wedding, filing the report of marriage at the consulate and amending her passport.  Just amending her passport was worth going there.   That part is much longer in the Phils.  The USEM will accept the Hong Kong Marriage certificate.  When we looked at doing in in Phils it was going to take 5 to 8 weeks give or take for the approvals.

My Filipina wife and I found it was easier and quicker and actually cheaper to marry in Hong Kong this past March.  We sent in the marriage paperwork 2 weeks before and spent about 5 days in HK for the wedding, filing the report of marriage at the consulate and amending her passport.  Just amending her passport was worth going there.   That part is much longer in the Phils.  The USEM will accept the Hong Kong Marriage certificate.  When we looked at doing in in Phils it was going to take 5 to 8 weeks give or take for the approvals.