L.B.
Puppies bite everything!! Especially when they are teething, which I suspect yours is. I used to raise Shih Tzu's and they are adorable.
I have a new puppy now too (Great Pyrenese) and she is also biting everything. I tap her on the nose and say "no bite." She is slowly learning. I have discovered one of the best discipline tools for a puppy is a spray bottle with water in it. They really don't like being sprayed in the face and after about a week all I have to do is pick up the bottle and the dogs scatter. LOL
As far as housetraining, if you don't have a crate, get one. The crate will become your best friend and your puppy's security place.
Puppies don't have the bladder control to hold it until they are about 4 to 5 months old. So yours should be able to be trained now. Mine was about 4 months old when I got her, but she was a big puppy and it only took about 2 weeks to housebreak her.
Take puppies out after they eat, after they nap, after they play and always take it to the same place and say the same thing. I say "go potty." Both my dogs know if I am tapping my foot and saying "go potty" that they need to go because they are getting ready to go in the crate so I can leave.
Good Luck!