#1 - I think it would depend how you plan to sell the car. If it's to a private party, they might balk at getting a title from another state, as it would complicate them being able to register. A dealer might know how to handle this better
#2 - probably not. It depends on your state what you need to do with the plate. Some states it stays with the car, sometimes it belongs to you.
If I were you, I would sell the car in your current state and rent something while you move. In California, the registration stays with the car, so someone buying it while there is still 10 months on it, would value the savings they'll get.