Ok! Here we go!
1: I really have not looked into it, but I am guessing about 24 hours. It seems to be there when I would check on the weekends. Which was around 3:00 P.M.
2: You mean the propaganda carts? Again I have not checked! I've only exploded about 2-3. My best guess is somewhere between 1-5 hours.
3: This one I know! Around 5-10 minutes.
4: This one is tough! I am guessing 3 days?
5: Lens cannot be picked up. You can only get Lens through battles. Cogs, Springs, Pipes, Cans, Apple Cores, and Banana Peels re-spawn in 2-5 minutes. Solvent usually re-spawns in 2 days.
6: 3 months.
Someone else will probably have more precise times.
Hope it helps a bit!