Are there any programs that can generate a huge amount of different interesting chess puzzles? Are there any programs that can make a lot of retrograde analysis problems?
AFAIK, there aren't programs that generate chess puzzles. On the other hand, there are several well known programs to verify chess problems (even with fairy chess conditions).
The main reason is that composing a good problem is kind of an art, the problem should not only be valid (in the sense that it is solvable etc.) but also esthetically pleasing. It also should be original, showing something new or fresh. These aspects are badly handled by computer programs upto now.