Is it permissible for me to take the books that someone brought for me from customs, the number of parts of which differs from the original books I bought, and also to take additional books from customs that would have been damaged?

These books likely belong to someone who either took your books in exchange, or they are lost from another person, and your books were stolen or lost.

If you find out through customs or others that the owner of these books is the one who took your books, then you may keep them in lieu of your books. This is known as "retrieving one's right." However, if you do not find a way to ascertain that the owner of these books is the one who took your books, then it is not permissible for you to take them, based on the Almighty's saying: "And do not consume your properties among yourselves by falsehood," and the Prophet's (peace be upon him) saying: "The property of a Muslim is not lawful except with his willing consent." The fact that the books are exposed to damage does not justify your taking them, because their owner might still reach them.