Is this a thing? Atheism by definition is the disbelief (or disinterest) in gods. So is it possible for someone to feel this way and still believe in spirits of nature?
Pantheism can be materialistic, so yes, some Atheists can be materialistic Pantheists which is still spiritual all on its own even without counting in the spirits of nature.
Yes. That would be Buddhism.
Animism itself doesn’t require gods, though many religions which possess animism as core aspects usually do have gods. But it’s certainly not a necessity.