Our book management software
permit manage books, permit manage authors, but I not understand what you mean under "sub-libraries within main library" ?
is it possible to assign another user to the same book thus increasing quantity
Sorry, this is impossible, when you move some book to lend - you move some exactly book. Every book has self owner and has self lend history.
Every user (or admin) self add book and all info about book.
With help Amazon API or openlibrary.org API - you may fetch some info about book
Q2: Is it possible for users to lend a book from each other without confirmation from library admin and even without notifying him?
Book Library - only interface for manage books or for manage lend. Some body must give real book. Approve may do as admin and as book owner. You may configure - notify to owner( to admin) when some body create rent request.
Q3: as I understand, users are able to enter books and use above mentioned scenario from frontend without installing and using Community Builder?
Yes, if admin permit this