You need a permit to trap or kill an alligator in Florida. However in a situation like this I wouldn’t hesitate to kill one by any means necessary.....also, feeding them is against the law.
I wouldn’t either, but that doesn’t mean you won’t face an inquisition afterwards.
Yes just ask the nearest illegal immigrant to refer you to his documents provider and ask for an alligator license.
Feeding them? I think they do a pretty good job of that all by themselves!