Everyone who has a cat knows how they like to do things like jump on the table and try to take your food. Do they just naturally share food? I think of like a pride of lions when they kill a gazelle and the whole pride starts eating it. But cats are supposed to be territorial so I don't know.

Your domestic housecat is closer in lineage to a small cat like a bobcat, lynx, puma or something like that. It would be more like those cats in a nature (if they weren't domesticated) than lions or tigers.

Yes but they have a hierarchy don't they? The male eats first, then the next in line and so on