Book travel in passport name. You must use the US passport to enter and leave the country. I would book in US passport name. Carry original proof of name change
Once the number is issued it's yours forever. SSA won't issue a card with less than 15 days left on I94. Also appointment is required now to go in person
If they reject they will send whole package back. Highly recommend to use personal checks for tracking and peace of mind. Also please complete your timelines.
Please complete your timelines. Once you get case number from nvc, check to see if ready at embassy. Once ready at embassy schedule medical and interview.