I'm working on a 1986 RX7, it comes with an auto tranny

problems
1. The shifter is really loose for some reason. like i can move it around really easily and shake it easily

2. it can go into all gears, N,D,R,1,2 without the brake being applied. even when the engine is on. odd?

3. now when i put the car into reverse and i'm on a sort of steep driveway. the car dies. and after taking a look. the engine seems fine. no vacuum leaks i can see. so can it be the tranny?

any ideas?