If your going to purchase a Posi unit in the housing take along a dial indicator and rig it so you can check the run out. This will tell you a lot.

Place a long mirror under the car so you can see the drive shaft and Rear axle housing. Have a friend nail the throttle while you watch and see if the angles are correct.

If you have a completely stripped philips head screw use a sawsall with a short fine tooth blade to carefully cut a slot in the head for a flat bladed screwdriver.

Don't waste good fluids, use a clean catch pan to corral it. Once done with the repair pour it back in using a painters funnel with strainer.