Demise

Got an interview notice. That's annoying, I thought that getting an RFE for medicals means it was waived. Oh well.

No. "US Person" means solely from the tax law perspective and that includes permanent residents and then everyone else that has lived more than enough days in US to be considered a resident for taxation, pretty much in order to be considered a "non-resident alien" and get to skip on taxes you have to essentially come and go very infrequently. So yeah, she can sign it without any issues, she's claiming to be "or US person" so there's no false claim of citizenship going on here.

The green card being produced is a bit of a legal fiction from USCIS. That's just when they order it to be printed, it likely doesn't exist until the day when they mail it out.

Then there's no underlying petition in that case. Part 2, she'll tick box 1.f. box 1 for "The Cuban Adjustment Act", Part 2, items 3 for the receipt number and date of the underlying petition will just be left blank or she can write "N/A" in there.

Yeah that's the C31 EAD. Basically there's a box on the I-360 for VAWA cases "I'm in the United States and request an Employment Authorization Document" if you tick it, upon I-360 approval they will issue you a C31 EAD. You can have multiple EADs, just use the C09 one since it's the better deal.

Block her and forget her, if she keeps trying otherwise then get a family lawyer and have them send her a cease and desist, followed by filing a no contact or restraining order. USCIS is prohibited by law from taking anything the abuser says into account for VAWA cases, similarly USCIS as a matter of policy doesn't take former spouses seriously because if they had to investigate every marriage that went sideways with a salty US Citizen then that'd be literally the only thing they'd be doing.

Biggest issue is just getting there. Probably should designate Almaty, Kazakhstan or Tashkent, Uzbekistan as the processing post. Warsaw, Poland is the currently designated as the processing post for Russian citizens but Poland basically bans Russians from entry, though that could be worked around by flying to any other Schengen Zone country (e.g. Germany) and crossing over the border into Poland (internal borders for Schengen are unstaffed and don't perform any kind of inspection). Alternatively you could probably just put Moscow, Russia as the post and deal with it once the time for an interview comes. What you put on the I-130 is more of gentle suggestion than a strict requirement on the state department, they will schedule it wherever they see fit and if that doesn't work for you for any reason you have to argue with the state department to move it elsewhere. Only thing that designating the post on the form does is tell USCIS "this person is abroad, forward this I-130 to the national visa center on approval" with the alternate option being "this person is in US, hold onto it for AOS".

You probably are, it's common for one spouse to take another's last name on marriage (generally wife taking husband's with other options being possible), if the photos and dob match, and you have a marriage certificate that bridges the two names then the airline will understand that this is the same person. Their biggest concern is boarding people who are not authorized the enter US because they get fined for that.