I am sure he loves you if he barks when you leave that is showing you he doesn't want you out of his sight
The nipping and biting is normal he's a puppy Georgie did the same thing. Tell him no give him his toy to bite. As far as backing away when you pick him up it's nice to know I am not alone Georgie is 7 and still does it! Believe me he loves you one day when he wont let you go potty alone you will think back to when you wondered if he loved you.