About "bits of" and "hang on the tree"

"Bits of plastic bags hung on the tree."

I am puzzled in two points about the sentence.

a) Can "bits of" be used in countable nouns? (bits of bags?)

b) About the preposition before "tree", I've been taught that for the thing that doesn't belong to the tree, "in the tree" is used; for the thing that grows out of the tree, "on the tree" is used. Then is "on" in the sentence used correctly, since it is related to the "plastic bags"?

Thanks for your help!

1. Yes, you can have "bits" of anything, countable or uncountable.

2. Yes, apples grow on trees and birds live in trees. But we hang Christmas ornaments on the tree.

:up: But remember that while birds live in trees they perch on branches - or sing, land... (But those two verbs can take either preposition - with different meanings. Birds both sing in trees (often you can't see them) but also sing on branches. And a bird can land in a tree or on a branch. You can't just draw up a list of 'nouns/verbs that take in/on'. You have to consider the context.

b