People use the leaves to make a health drink, a "tea". (It's supposed to help with cancer.) So I'd say that the leaves are reasonably palatable and goats would probably eat them. But I don't know from direct experience.

Not that I'm aware of; the papayin enzyme in the fresh leaves gives them a stomach ache. The tea infusion is drunk in small quantities to alleviate digestive problems.

My neighbors have goats

I was wondering if I should fence around my trees from the goat or just let them grow

I dunno- goats are unpredictable. I thought you were asking if you should feed papaya leaves to goats. You never know what a goat is going to do. Maybe just put a net over it until it grows tall enough that they can't stand on the trunk and crop the top? Cheaper than fencing.

Lol........silly goats