Yep, I'm a spud!
I've only lived here a year though, so I don't think it counts yet!
I have no idea what kind of tree that is, but the leaves look like cherry tree leaves to me. I've never heard that it isn't okay for chickens to eat cherries. Lots of friends have chickens who eat the cherries that fall off of the trees, and they love them. None of the friends has lost a chicken yet.
I have a bunch of trees on our property that have fruit that looks somewhat like cherries, but the leaves are different than what you have. I need to get an ID on my trees one of these days.