This would be akin to asking a shop owner if I'm allowed to pick a panflet from an endless stack of panflets placed on the sidewalk. If they don't want the public to pick panflets, don't put them where the public can reach'em!
I’m not sure taking liberties with things you don’t own, is always the best policy, nor is putting the entire responsibility on the owner.
I don’t think this is something you can boil down to a simple black and white.
If you put a server on the public internet and I send it a message (assuming I’m not using ill-gotten credentials, etc.), anything it responds with is your problem, not mine.
No. It could be said, but wouldn't be true - objects in a domestic front yard are nothing like pamphlets placed on the sidewalk.
Not sure why you are acting so obtuse.