A. The motor will turn an m120 just fine.
B. The lipo will turn the motor fast enough to turn the m120 over just fine.
C. There is no problem with doing this with a low-power spring. You will be fine. It IS overkill for your needs, but will NOT kill your 'box.
Standard wiring has the battery plug straight into the wires. The trigger is simply a switch. One of those wires runs directly to the motor, the other goes to the trigger, across a gap that is closed when you pull the trigger, and down another wire to the motor. It's pretty darn close to the simplest DC circuit you could make.