As far as a cat,it you take that route you want a female cat. The male does not hunt.
Nature is clear. No transgender etc, debates. The way it is is not debatable.

Far from a poop expert but that is a lot of poop. Several days or several animals. Breeding? If, mothballs do not work, try Chayann pepper. Since you have not seen them they are repelled by people. Try leaving a talk radio show on all night. You can use glue traps. You can use rat traps. The question is the proper bait. Peanut butter? Bacon, seriously most animals like bacon.

That’s when the For Sale sign goes in the window. I would do that when I return from the hospital for my heart attack.