Kleio
Regarding Hunting and Gathering.
If I player claims 5 squares I accept that though I think it silly. I claim the tiles next to any of my cities and any square I have sov on. If a kill is occupied by my army it is mine. The exception to that is if I attacked a square but someone else gets there first and I knock them off. The kill is still the first player to the square.
I do not intentionally bump anyone else off a kill unless it is my kill next to my city or in my sov. Accidents of timing happen. Message me if we have a conflict.
I do not recognize a claim of more than 5 squares from a city unless the square is occupied or under sov.
If it is clear to me that a kill was made by a player, and not another npc, I leave it alone. Occupied by troops or harvesters or gear on the square is how I tell if the kill is another player's.
This is not an exhaustive list of all that can happen and my response. It does cover most of what happens I hope.