Also, what's up with their own secure library at the Vatican? Shouldn't they be giving the old artifacts, books,etc to museums?

The Vatican libraries date back roughly 500 years, depending on which official start date you prefer. The Vatican is a sovereign state as well as being the home of the head of the Catholic Church, and the modern Vatican libraries are generally highly respected. They are careful with their collections and have some arcane policies, but most archives share those attributes. The Vatican standard of waiting 75 years before releasing the documents of a given pontiff is a bit of an oddity, but it reflects the generally cautious nature of the institution. If you are referring to the "secret" archives, the term is closer to "private" like a "secretary" rather than referring to something that is hidden. There are requirements in place to be able to access these archives, but they aren't impossible to meet by any means. Also, the Vatican itself maintains a large number of museums that are open to the public.