The Walkers aren't supernatural, but what they are
is paradigm shifting. They're new scientific data that would radically overhaul existing scientific theories if there are still scientists around working on those.
You can't really compare the barn to a mental hospital because even those in there can still reason, speak, and aren't constantly trying to eat other people unaffected by their "disease".
No, I still can. I could compare it to a hypothetical mental hospital inhabited by dangerous and unreasoning insane subjects with a cannibalistic taste for human flesh.
you can bet that some killing would happen.
No doubt. On this point, I'd observe the Otis is perfectly okay with killing zombies at the school, because it's basically a necessity.