Hello and welcome to YT!
I for one really think "puppy kindergarten" or puppy training classes are a great idea for a puppy. As soon as my youngest, Tia gets the rest of her shots, I am signing her up!
As to the rest, I don't really have anything to add. The biting is annoying, but unfortunately it's how they play. If Tia bites, I YELP like a dog in pain would and she quits it right away. That's what is working for us so far