I had the same problem with Lady... well she's 6 months old now and she's still hyper. But the biting in particular was a problem (as you say - sharp little teeth!). I was able to correct the biting by saying a loud 'ouch' everytime she bit me and ignoring her for about a minute. I did a lot of research to get advice as to what to do and tried a lot of things, but this was the only thing that worked and she stopped biting after about a week of consistently saying 'ouch' each time she did it.
As for the crazy puppy behaviour, I can't really help - Lady still chews anything and everything (my bedroom floor is currently covered with ripped up paper) and runs around like crazy. I hear they grow out of it eventually... but you might be in for a long wait.
Mummy to Lady (Blenheim Cavalier) and Lola (Silver Tabby British Shorthair)