To answer your question as to whether the motor hooked directly to the battery of your car would over load it, it would not unless it was directly shorted out. There is no difference in wiring it directly or thru the vehicles wire harness unless there is a resistor somewhere in the line~ typically not~ and it would show up in the wiring diagram. Also a 9v battery may not have the potential to run a 12v motor and if it did it would not run very long.
SD51 made the observation that your motor should have a resistance of around 2 ohms, most good motors have a very low resistance, so at 250 ohms its definitely burnt out as the increased resistance lowers total current required to drive the motor. My thoughts.
