On the parking bit, I generally see amenity=parking covering a whole parking lot, not each row. This may be a local to me thing, but it’s also what I generally see. There’s a way to mark invisible spaces too if desired.
For the natural=wood bit, that also seems weird, there’s ways to mark trees and gardens, I’d look at the wiki for what seems to match the best and suggest/retag as that. Natural=wood may fit though, not having looked myself.
