Is my puppy rude, or is he normal?

My puppy (Pluto M) is 2 months old. His teeth have grown and I think as what I’ve experienced before, biting at this age is normal because of his teeth growing. He keeps biting everything he sees, my hands, my legs, my shoes, my toes, the wires, everything. He doesn’t play with his toys. However, this isn’t the only issue I have with him. When I tell him “No bite!” he will bark at me loudly! And when I pet him, he automatically bites my hand. He doesn’t bite too hard but it hurts because his teeth are sharp. He talks back at me rudely (shouting)...

He has a puppy friend (Maya F) who visits 3x a week and when they play he bites her so hard he makes her cry. We have to pull him off from her because he doesn’t stop. Also, Pluto shouts at my other dog (Sumi F) who’s 5 yrs old. He will stand in front of her and bark at her face. She just ignores him, sometimes she growls at him but Pluto doesn’t seem to care at all and will just continue.

Long ago we had a puppy who kept biting (he doesn’t listen when we say “no bite” too no matter what we say) until he grew up and he thought that biting is a play so he just keeps on biting biting biting w/c left me scratches all over my arms, legs and my face. I don’t want Pluto to grew up like that. I want to discipline my puppy but I don’t want to hurt him, not that way. He listens to me sometimes and I give him treats if he does. Is his talking back to me in a rude way normal? What should I do? What’s the best way to train my puppy to be a nice puppy? Our other puppies don’t seem to be as naughty as him, they just play nicely, listen and lick you in the face.

(My mother has a shop and there’s a dog who lingers around her shop. Pluto is that dog’s son, we adopted Pluto so I’m not sure of his breed. He’s just like this puppy but he has pink nose)

Also, I’m sorry for my bad English, it’s not my first language