In regards to the first part of your question, here's a video that shows what might go into the book boxes, including numbers of books.  https://www.thedailycafe.com/content/book-boxes 

There really is no absolute number of books, but students need enough books to keep them engaged through a round of Daily 5.  For younger readers, whose books are shorter, that's going to mean more books.  Older students who are reading chapter books may ony need a few different kinds to keep their interest.  Changing books often enough to always have engaging titles is also important.  

To address the second question you have, check out this article with ideas about how to approach such a student.  https://www.thedailycafe.com/content/abandoned-books-and-lack-engagement... There are other articles linked there that might be of interest, as well.