(1) If we are married in NYC can she sue for divorce in Russia?
(2) Is the NYC marriage (apostille document) recognized in Russia without any additional paperwork?
(3) Is the apostille document enough to change her Russian passport last name to mine and show she is married?
(4) Final question: if she does, what happens with a prenuptial US contract that we have in NYC?
1. Yes, she can file divorce in Russia. You can do it also.
2. Yes, NY marriage certificate with apostille you can use in Russia without any problem. You just need to make official translation.
3. Your wife can change her domestic Russian passport without any problem. She need to show the marriage certificate with apostille and Russian translation. It will be enough.
4. Nothing. Your prenup is legal. She can put an apostille for prenup, make Russian translation, and file it to the Russian court, if she wants.