Haven't you heard of Cullenism? It's a religion that takes Stephenie Meyers' thinly veiled Mormon propaganda as it's holy text and believes that the Cullens are real and heaven is being able to spend eternity with them.
Also, yes there are people who file down their teeth and believe they are vampires, they've been around longer than Twilight.
Yes, there are also children who have asked Robert Pattinson to bite them. Also, girls who have scratched bloody holes in their necks and then walked up to him to say they did it for him. I've heard that he's been quoted as saying that he wishes he had never done the Twilight series and personally, if I was him I'd feel the same way.
Most kids are idiots. Sadly, the parents are also idiots and indulge their children in these delusional behaviors. Remember the girl I mentioned that asked RPattz to bite her? When he said no, the child's mother freaked out on him and demanded to know why he wouldn't bite her child.