1.) She was at-fault which Police documented. Should I file with her insurance (State Farm) or mine (Geico) and work to get reimbursed?
Contact you insurance and give them all the details.

2.) In terms of body work, would you recommend that I take to a dealer or a body shop? I think BMW of Fairfax has a collision center.
Call your (reputable) dealer and ask them what collision center they use/recommend.

3.) Anything else I should know? I've babied this car and hope that the repairs will restore her to back to where she was.
Looks like a lot of $$$$ and may be close to the 75%. Make sure there is no frame damage.

good luck!