It's important to remember that this is just a puppy and will have puppy behaviors for quite some time. And, your puppy is quite young to be without her mom and littermates, so the transitions may be a little more difficult.
I know that when our Bella clamped down on my fingers, I let out an , "owwwww" and that stopped her in her tracks. When your pup starts to chew or bite on things that are not okay, immediately redirect the behavior to something that is okay for her to chew on.. a rubber toy, chewie, etc..
It is never too early to start training. Just don't go overboard with it. your puppy needs to be a puppy.
We got Bella on Tuesday and she is 12 weeks old, she's pretty comfortable with her name and is learning sit and come now. But these are not rigorous training sessions.
Good luck!
P.S. --- puppies do sleep... A LOT!!!