I'm sure that someone else will be able to give you more thorough answers to your questions; but I can answer what I do know:
I also have noticed problems reoccur, though I am not sure if they are the EXACT same or perhaps just very similar (this has helped my rating though, so I'm not sure if I want that to change!).
It seems that some of the problems do have more than one answer, but my experience has been that the 'correct' solution is either more forcing or leads to a more definative result (perhaps instead of one line that leads to being up a queen, there is an alternate line that leads directly to mate). If you find a problem that has multiple 'correct' lines as you said, you are encouraged to inform chess.com of the specific problem and the line that you see.
I think Chess Mentor has an ending course.
Hope that helps!
I have some questions concerning tactics trainer. When you get a problem wrong, will chess trainer eventually show you this problem again until you finally get it right?
Also there are a few bugs in tactics trainer such as some problems seemingly having more than one answer. Will these eventually be rectified.
In tactics trainer, when you successfully complete a problem, it tells you how many attempts have been made, and the success rate. Is the number of attempts cumulative? Or is it only the number of attempts made that day?
Also, is there a place on Chess.com to study endings? How is the proposed openings site coming along?