The biting thing is 100% normal...at least it was for Bella. I couldn't even hold her because she wanted to bite everything nonstop. She bit everything!
I don't think you have anything to worry about, but I'm far from an expert. Bella has done everything your puppy is doing and she's a very sweet dog now, at 6 months old.
She still ignores me occassionally, unless I have something to put in her mouth.