Are you allowed to read books on youtube?

There are definitely some authors out there that would like the free exposure. Perhaps try for up and coming authors and books that are just seeking to get exposure. Plus, since they're just trying to get out there, they may be interested in some sort of collaboration. They could also provide exposure for your content as well. Win-win for a lot of people.
When I wrote a book I asked bloggers with the most views and an appropriate audience to read my book out loud and discuss it with their kids. So, if you want to build content on book reviews, I guess you have to contact the writer and discuss the issue with him or her. I am not sure about old books though. You have to ask the publisher for permission as they hold rights on the books as well.