@slipstick - I do know that I cant use the Arduino to power the motor. Thanks for the info regarding the common ground. I was afraid that if lets say 1A passes trough the Arduino GND, it will fry it.
If you are not drawing motor power through the Arduino and if you have the Arduino GND connected to a common GND the only current that will flow in the Arduino GND pin is the return current for the Arduino itself.In response to your other Questions1. yes the motor current will increase as the load increases.2. yes. I would describe "the input voltage - the voltage drop of L293D" as the voltage available to drive the motor.3. the driver will be damaged when it overheats - with a bit of luck that won't be instantaneous, but don't count on that.Torque in a DC motor is created by the current flowing in the coils. When a DC motor is running it generates an internal reverse voltage that opposes the power supply voltage. The maximum speed of the motor is reached when the difference between the reverse voltage and the supply voltage is just sufficient to allow a current to flow that generates just enough torque to overcome friction at that speed. Hence a higher power supply voltage will give a higher no-load speed. When you apply a load to the motor it slows down so the internally generated reverse voltage declines and more current can flow. The extra current generates extra torque that helps to offset the extra load. When the motor is completely stalled there is not internal reverse current and the only thing limiting the stall current is the resistance in the coils. For many motors the stall current is sufficient to overheat the coils and damage the motor....R