Hmm in terms of peeing, I think 3x a day for a puppy is way too few. Check out the pinned housebreaking thread. It's a slow but sure process and whenever he pees properly, let him know that he's a good boy/give treat. Try to redirect his biting and chewing (perhaps because he's teething) with teething rubber toys and icecubes.
When you're at home, try this: put him in the playpen and if he starts whining/barking, ignore him / turn your back / walk away from him. Timing is important here, the second he stops whining (hopefully he will take a second to recoup energy
), approach him, pet, praise and play with him and give him treats. Do this often enough until he gets that being quiet = rewards, being loud gets him nowhere.
With separation anxiety, I have tried this: I go out of the door quietly (I don't say goodbye, hug or make a huge deal of it), and come back after 5 minutes and if he's quiet, more praise and treats. Extend 5 minutes to 15 and so on. He'll soon realise that you'll always come back (with treats) and not leave him forever in a playpen.