I would change both CV joints and the bottom motor/tranny mount. My 2000 was doing the same thing and this did the trick. Around $400 for a shop to do it with parts. $200 just for parts if you do it yourself. Good luck.

 

Re: Reverse not engaging,
Mine did this a couple of years ago and I changed the fluid and no problems since. I think if was dirt stuck in a valve that allowed the fluid to drain off after sitting. It was doing the exact same thing you described...