He may take a book from the library if he finds what he is looking for. -very informal. He may take a book from the library if they have what he needs. If the book he needs exists, he may take it from the library. If the book he needs exists he may borrow it from the library. We borrow books from libraries in the U.S.A. "Take" might imply stealing.

Я бы сказал так: "He takes a book from the library if there was the right book"

Then what about to replace"was" on "is": "He takes a book from the library if such a book is there"? I wanna say about regular action.

He takes a book from the library if such a book a was there. Sounds better, I think.

"He takes a book in the library if needed, do books exist there?"