More context is needed to tell whether 1 means something closer to 2 or 3.
2. suggests that the being sorry and the not being rich occurred at the same time in the past. 3. suggests that the not being rich occurred at some time before the being sorry about it, and that there was some relevant intervening fact (as one would expect with the past perfect). 1. is ambiguous about this, but the context would help.
4. No. I would say "I wished I was rich".
Yes you can change it with 5. if you think nothing would be lost in meaning, as per my first line.