I was a weird child and my parents saw that I didn't really fit in. So at a young age, they took me to see his movies, and I'm thankful they did. Tim Burton has been my mentor ever since haha! I even went to his exhibit at MoMa (it was amazing!!!) So I think kids should definitely see his stuff, you never know.
And yes, it's a remake of his short live action movie. He's redoing it because now it can be done the way he wanted without money getting in the way, like last time!
Yes this was his first major piece. If you own the original Nightmare Before Christmas DVD, it has it on it. I loved it, but I have no clue why he'd remake it.