If your parked car was hit in the rear and the person who hit you has no license or insurance who is responsible for the damage to your vehicle and the medical bills for any injuries?

Well the person that hit you is not responsible enough to drive with insurance, if someone was in your parked car, you would still be responsible,its your car after all. The person that hit your car would be liable and you would have to go after them legally. If the uninsured driver in fact gets injured he will be responsible for himself, insurance companies are not in the business of paying people who drive illegally.