My MC's best friend from childhood was raised in the US illegally and doesn't find out he's illegal until he's an adult. My MC marries him in order to help him obtain his residency and pursue naturalization.
Do the interviews/interrogations of the fiance/spouse really happen the way you see in the movies? For example The Proposal. Would my MC actually have to have an intimate, sexual relationship with him in order to verify details she might not know otherwise?? She's his best friend so she knows pretty much everything else about him.
Oh hey, this one I've done personally.
So let's see, first thing that pops out at me - if INS realizes he was here illegally, often they will make him leave the country for a prescribed period of time then request to re-enter again, in a legal manner. My mom had a good friend who was here and married to a citizen for a few years, then something came up about her initial entry into the country and she was forced to go back to Georgia (the Russian one) for a year before she was able to request re-entry, despite being married to a citizen. She was allowed to come back after that and her greencard is current now. I'm sure in your story you can get the INS to make an exception for your character to get around this, but just FYI, that's an issue.
Second, yes, the interviews and information they require are intensive and invasive. My ex-husband and I waited eighteen months after we were married before he applied for his greencard (he had been here on a student F1 visa ever since he was 10). At that point I was seven months pregnant with my daughter. Despite being pregnant with his child (and married for awhile already), they still grilled us. It wasn't quite as bad as the scene in that movie Green Card with Depardieu, but it was still pretty intense. So yes - your characters will need to work hard to establish what appears to be intimacy. I also remember putting together a photo album to establish our time together. I had actually known him all through high school and college, but it was still tough to find enough pictures to make them happy.
Also worth noting, if they apply for the greencard before they have been married for two years, they have to go through the whole process twice. Anything before two years is a temporary greencard (which is an additional two years). At the end of the temp greencard you can apply for the permanent one, at which point there are new interviews. In theory they could deny the permanent greencard at that point. Being divorced already by that time may mean the greencard gets denied.