Hello there, Pitbulls are prone to Seperation Anxiety, so it sounds like thats what your pup is experiencing. How many hours a day do you leave him alone?
Someone replied to take short trips and come back, letting him know that you are coming back and not to worry. That is 100% correct. Crate training is a must for pittys that suffer from seperation anxiety. You will find him starting to tear things up unless you get him in a crate in a safe area. I'm sure you do not want the expensive vet bills for removing foreign objects from his stomach.
You should defintely enroll your pup in obdience training, it sounds like he's taking advantage of your kindness. I can defintely recomend some pit friendly and pit expierenced trainers in your area if you send me an email.
The puppy nipping must be stopped. I do this by giving my dogs a time out. If the pups I take in nip, they get put in their crate for 5 mins all by themselves. Pitbulls need and want to be with people is so strong, that this is the best form of punishment.
If you have any more questions, feel free to send me an email at firstname.lastname@example.org
. I'm the President of the Positive Pit Bull Awareness Society, and I can defintely help you out.