Hi,
Can i run a 12V motor on 9.6V battery?
Yes, but it will be slower of course.
Can i run a 12V motor on 9.6V battery? If so does it cause the motor to draw more amps?
Just apply a little Ohms Law here...
Assuming the motor takes eg. 2A at 12V. That means that the equivalent DC resistance of the (running) motor is 12/2=6 Ohm
If you apply 9V over 6 Ohm, the current will be just 9/6=1.5A
So, current is reduced, but worse, power is reduced by the square. At 9V it leaves only (9/12)^2=0.56 times the power at 12V.