I could be wrong but Charlie knows about vampires.
They had to explain his 2 year old grand daughter.
Charlie just doesn't want to know about wolves and vampires. It has been awhile I think that I am right if not then they have to tell him.
No, because that would make the Volturi either kill Charlie or force him to be turned into a vampire, once they found out that they know. And Charlie doesn't want to know any details. He just knows that they're somehow different, and that it was done to Bella to save her life.