Your answers await you in the BA forum

Basically if on two tickets no

If on one ticket yes they will check bags, will you make the flight ? God knows but SFO is a nice place to enter the USA, but my experience isn't holiday times.

Is your BA F paid or avios ? If avios you could look to see if you could change to an entry point that AA serves your final destination from which would make things simpler for you as BA will thru check onto AA or any other OW airlines.

Good luck.
cs