The "most" trouble I think you'd get in is if the police or someone notice a non-state car parked in the same place for a long period of time. (Be it your driveway or apartment parking lot, whatever type of residence you live in.) Then you might get a ticket in which case you go to the traffic court, explain that it's not your car and you're borrowing it from out-of-state owners. Either the ticket will be dismissed or you'll pay an annoying fine, more likely the former.
Not if she's close to a college. I got the impression the Bay Area has a good number of universities and colleges when I was looking into a teaching job over there, last spring.