Yes you will have to modify the flywheel for the sensor, but otherwise it should work.

The driveshaft from the donor car should work.

The way you describe it I would fully expect that the problem with the donor transmission is the shifter, the shifter bushings in general. These are replacable.

The motor mounts are different in their elasticity because of the way that a stick shift transfers torque the mounts when starting from a dead stop. It's not mandatory that you use them but if they are in good shape I would prefer the ones from the donor car. I'm pretty sure that they will fit your 104 engine.

Good luck,