Please complete your timelines. Unclear where you are in the process. If already in USA, AoS interview would want to see evidence of married life living together. Bank accounts, health insurance, emergency contact details at work etc.
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