Stopping the motor from turning results in a short curcuit in one of the armature coils. If sufficient heat builds up, it will burn out the coil. The car will still run on two coils, but will produce 2/3rds the power (two of three coils are working). It will also stutter.
As for the second part of the question, if the car doesn’t have enough power to get up the hill at the end of a charge, it probably won’t burn out the motor, but certainly will not help it either. If the pinoin were slipping, you would be able to hear the motor turning.
