Yep, problem one sounds like shimming.Try to eliminate the play in the front.It may take some custom shimming to tighten the mesh...and you may not have quite as free a driveline ,but it helps save gears.
Problem 2 simple.....
A. get the heavy duty drive cups or put a lil plastic under the drive cup to tighten them up!
B. and this will help with problem one also....Stop hitting stuff.
Think about where the energy goes when you tap something.The ball cups on the rear absorb all the energy form a hit.The cup under the tire cannot pop off so the inside cup pops off.