Need help understanding K1 post-marriage forms & procedures

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My K1 fiancé and I were married one week ago. An additional complication in our case (admittedly not uncommon) is that she has a son still in her home country of Russia. We intend to bring him here this year, preferably by June. That will involve her traveling back to Russia, to help him with the process. (He's just 16.) Another more immediate issue is that we want to travel outside the U.S. in a few weeks, for a brief vacation. I haven't yet filed any forms since the K1 process. So, from all that, here are my questions:

1. Name change. If she will take my last name (replacing a last name from a former marriage in Russia), at what level and with what form is that done? Is it part of the SS# filing process, or must it precende that? And most importantly: Does that need to be done BEFORE any other forms are submitted, so as to implement her new married name consistently on everything that follows the K1?

2. Form 131. I assume from what I've read that this reentry permit process is required for ANY travel outside the U.S., not just travel back to the home country. We want to go to Dominican Republic in the 2nd week of March, which is only about 2 weeks from now. Is it feasible to accomplish this in such a short time? How?

3. K2 visa for her son. I have been informed by the U.S. Consulate in Moscow, about what documents will be needed for her son. However they haven't made it clear what sort of timeline to expect. Specifically, the time between request for an interview for her son, granting of the interview date, and how long after the interview will he actually be able to travel.

My great appreciation for any help you can provide!