EM_Vandaveer

If the reason for his refusal is that he doesn't have those papers because he never obtained a divorce (hopefully this isn't the case) then unfortunately your marriage would be invalid and you would not be eligible for AOS neither through him nor via VAWA as you need a valid marriage for either of those options.

You do need to obtain a divorce.

They should file ASAP.

Nothing happens automatically, however the beneficiary is deportable so if for some reason they come into contact with ICE/CBP/Border Patrol they can be detained and deportation proceedings can start against them. Marriage itself confers no immigration benefit, once the 90 days are up the beneficiary is overstaying.

You'll only need the I-864 when you file for AOS in the US. For K-1 you need an I-134, you need that for the interview.

There is no such thing as "registering an already existing marriage in the US". On the other hand married IS married. Therefore if you ever have to prove you're married and you got married in a foreign country then you show your foreign marriage certificate (with an English translation). It's sad that so many don't understand this concept although it's logical. For example, bigamy is illegal in the US. If a marriage that took place abroad "wouldn't count" in the US then a person could just get married to a second person in the US even though they were already married in another country to another person. Since that's obviously not allowed, it stands to reason that that is because the first marriage that took place in another country is nevertheless recognized as a legal marriage in the US...

Those 637 days were just waiting for his place in the queue to get an interview. They weren't investigating during that time. Now they're investigating (or rather they will once you give them the DS-5535). As frustrating as it is, you don't really have a choice but to fill out the DS-5535 and wait.

There is no ROC process for a parent, a parent receives a 10-year GC automatically.

The question, I believe, in plain English is asking "Are you inadmissible on those grounds?" So the answer to that is NO, according to what you wrote.

Wouldn't demonstrated immigrant intent make its approval unlikely?

no interview involved, we're talking about an I-90....

She demonstrated immigrant intent so getting a tourist visa at this point is unlikely. One roundabout way I've seen mentioned (it usually works) is seeing the process through, getting the GC then turning around and officially abandoning it, thereby proving lack of immigrant intent and THEN applying for a tourist visa. It's a very pricey and time-consuming way of getting a tourist visa, though.

Chances are those parents weren't beneficiaries of Immediate Relative petitions which don't allow for derivatives. 1. is quicker, the parents should also file for re-entry permits which will allow them to leave the US for up to 2 years without losing their LPR status so they can wait with their son for his process in the home country.

Legalese at its finest, indeed. You are right, they should.

It's not a maybe, it's a no. It clearly states that the part of the process the expedite would help (getting your case assigned to an officer) has already happened. The rest of the process cannot be expedited. You're right, not helpful at all.

That makes no sense, to be honest. She's not required or eligible to file I-751. It's not a question of choice. The correct procedure is to get the GC corrected via I-90.

Is her income US-based? Because if not, she cannot use that income to qualify.

You can't file I-485 before you have your waiver, it'd be denied.

Wouldn't NVC see through this, though?

TX is one of those states. I actually had trouble in another country, I had my TX marriage license (this is what it still says on top, but if one reads the whole document, it's clear I'm married), with a duly added apostille & the clerk took one look at it and said "This does not prove you are married this is just a permission to get married" & so far, no amount of explanation "of course it proves it, I received a GC and later US citizenship based on this marriage" has yet been successful.... Maybe next time when I try, I get so frustrated I give up on it for months (ironically it's to do with immigration to this other country LOL)

FYI having a lawyer does not, in any way, make the process quicker. I echo other posters, consider marrying in Laos or a 3rd country & filing for a spousal visa instead. The timeline, filing to visa in hand, is similar but spousal visa is cheaper and your spouse will have LPR status (be able to work & travel) as soon as he arrives to the US on a spousal visa.

Not necessarily, sometimes it's just goes under the radar, OP certainly has nothing to lose by trying.

OP, there's your answer @almendez

Travel before November, have her get a new passport in Hungary.

you don't need a valid passport to apply for naturalization FYI, otherwise you're spot on