Do the rare/elite/minion illusions drop any loot? If so, is there a limit to how much loot illusions can drop from a single pack? I had the idea that it might be a valid strategy to continually kill illusions while leaving the real enemy alive, in hopes of loot farming, but I've never paid enough attention to see if illusions drop anything.
No, illusions don't give loot or experience.
Summoned monsters, however, do give loot and experience. It's generally not worth your time, though. It's more efficient to just kill them as fast as you can and keep pressing forward.