Hi and Welcome to YT!
First of all... no tapping the nose... just pisses them off and makes them want to bite more. lol! Redirect his attention to a toy and praise him when he shows interest and plays or bites on it. When he grows up and becomes an adult many of the puppy behaviors will disappear.
For everything else you mentioned... you would be best talking to your vet... he/she can run tests to figure out what may be going on with him. Once he gets a clean bill-of-health, then reaccess his behavior, as health problems can affect behavior.
Let us know how it goes! and Good Luck!
