I'm relieved to hear that rock-throwing is just a ploy to move the possum to a further tree, and no harm is intended. But! Possums are getting bad-mouthed in this thread. In their defense let me say: they have a place in nature, and they eat stuff that would otherwise just sit and get stinky. Eating from the rear is what scavengers without large teeth have to do if the hide on the dead item they have found is too tough for them to bite through - it has nothing to do with a preference for "dirt".
Wild animals occasionally catch diseases, as do domestic animals if they are not vaccinated, so it's important not to touch any animal that looks sick (for example: drooling, eyes watering, staggering, moving too slowly, or not showing fear) and keep your pets away from it too. Leprosy in possums I doubt - what would they catch it from? Canine distemper is a possibility, though.
When possums are frightened, they hiss, growl, or play dead to defend themselves. This is reasonable. A cornered cat will hiss, a cornered raccoon will snarl, a cornered skunk will spray, a cornered mouse will bite, they all just want you to go away and not hurt them.
