Can I use a spare Darlington Pair on my ULN2003A to drive a DC motor?
Should work just fine. But you'd have to connect the motor to the positive rail, and since the ULN2003 can only sink current.

Normally when connecting a motor, you'd add a flyback diode. But the ULN2003 already has those inside the chip.

PWM is the easiest way to (somewhat) control the speed of a DC motor.