I read books while IN a tree.
The word "in" is the preposition word (حروف الجر) that is usually used in this context. It's like you climbing up a tree and you are surrounded by the branches and you decide to read books.
If you say I read books INSIDE a tree.
It means you are really truly inside the main trunk of the tree.
If you say I read books ON a tree.
It means like you are the most top of the tree.
If you say I read books ABOVE the tree.
It is like you are floating over the tree and you read books.
So which word would you use?
I would use those words exactly as you have. As you have shown, it all depends on the situation and the meaning that you are trying to get across.
Some people might climb a tree to some branch and read a book while IN that tree; however all the other options that you have written seem rather unlikely scenarios. You have described all of them well.