:) Hi, as someone who has rebuilt automatic transmissions, The parking pawl is a positive metal to metal locking mechanism. It will hold much better than a parking brake. Because of the notches in the cog wheel being spaced out, and the size of the locking pin, your vehicle will move a bit. you should always use your parking brake when on a hill / incline, or when you want to hold your vehicle exactly where you stopped, like when lining up with the trailer ball.
The rear end, or differential, does not hold your vehicle and you should not have any movement in your "U" joints. You will have some slack in the differential. (ring & pinion) Turning one rear wheel and the other one going in the opposite direction is caused by the spider gears, AKA differential, is a simple basic way of telling if you have a locking differential or not. With a locking differential both rear wheels will turn in the same direction.