I'm going to address one of your problems, because I think they are completely unrelated and should be split into two separate questions. If you end up agreeing with this answer, I suggest you limit your question to that problem and split the other off into another question. If you add a comment when you've done so, I'll do my best to answer that one as well.
Puppies, like children, explore the world through their mouth. In fact, lacking opposable thumbs, this stays true for dogs all their life. But because puppies are not born with bite inhibition, the technical term for knowing how hard is too hard, they need to learn it.
When puppies grow up around their other litter mates, they will chew the living daylights out of each other's ears, noses and any other appendages. Whenever puppies are playing and one puppy chomps down too hard on another, the second puppy will naturally yelp in pain and stop playing for a bit. This way the first puppy learns that it bit too hard and will, over time, learn just how much force it can put into a bite.
When it comes to humans, whose skin is much frailer than dogs, we have to teach them that they basically can't use any force at all. In order to do this, you use exactly the same technique as another puppy would.
Start playing with your puppy to get it proper excited. Whenever your puppy takes your hand in its mouth and bites too hard, you give a quick, high-pitched yelp and stop playing, even going so far as to turn your back or leave the room for a second, if that's what it takes. Normally though, a yelp and stopping play should be enough.
Start playing again after a few seconds (<10) and keep repeating. Your puppy will soon learn that it can't bite hands with any force whatsoever.
If you don't want your puppy to take your hand in its mouth at all, I'd suggest just stopping play and removing attention whenever it does so. If you yelp in these instances as well, you might associate hands in his mouth with being bad, and that can turn into a problem when you (or your vet) have to check your dogs teeth or when you have to take that chicken bone out of its mouth that it managed to pick up on a walk.
Your puppy should be comfortable with being handled in all sorts of ways, and that includes having a hand in its mouth. But if you just stop playing every time it puts your hand in its mouth, it should learn that hands in its mouth only means no more play, so it won't do it by itself.