I never ask a park if it's ok to do the maintenance because if you're told "no" and get caught doing it anyway, you're going to be in trouble. However, if you don't ask and get caught doing the maintenance, you have the option of pleading dumb. With that said, I try to do the maintenance "low profile"--in other words I'll keep my tools under the RV, do the work on a Sunday when no maintenance or security guys are working, etc. I do make sure that I leave the lot as I found it. There are no oil stains on the cement, etc. If you do maintenance, I think you need to be responsible about it by not leaving a mess when you're done.
As for the dirty oil, etc, we've found that nearly every dump has a recycle section that allows you to leave used oil, etc, there.