I am drawing my own cartoon and I am also sending it to a very important celebrity, so how many should I draw to impress him :)?

One only. Celebrities get tons of stuff and most of them don't pay much attention to what's sent to them. Don't expect a letter back or anything. They just don't have the time to do that.

Are you a stalker or a fan?

One is sufficient.

Just send one. The 'celebrity' will most likely never see it, unless it is truly professional looking and good. Fan art is seen by assistants who will only forward the truly best works. Sending tons will not better your odds, they will lessen them. So send ONE piece, and make sure it is your very best work.