A small brush system ahead of the actual wheels could take care of some of the tree debris. Even a small to medium sized branch would probably have no effect, the tram is heavy enough to just cleave branches apart. The negative of that is the maintenance teams probably have to clear out stuff that gets stuck under the trams.

There are plenty wild animals in large cities. Foxes, rabits, racoons ... Berlin famously has a large boar population. Having a more human friendly city with green tram lines and less car traffic will surely increase animal populations. However I doubt it would be a problem that isn't easily solvable or is still preferable to the current situation.