Your puppy is a Laborador RETRIEVER. It is instinctual for them to be mouthy. Expect your lab to chew test just about EVERYTHING for the first two years.
The biting when being petted is just play antics. The first command I teach all my dogs is "No bite!" When the puppy bites, I remove their mouth, hold their mouth closed and say firmly, "No bite." All three of my dogs will play rough with me but if they get mouthy and I say "no bite" they will actually SPIT out my hand and start licking it.
You do NOT need to terrorize the puppy by holding it down and growling at it when a simple command and gentle holding of the face will do. This is the dog equivalent of a human infant. When your human child bites, you don't hold it down and yell at it, do you? You extricate the child and tell them "No."
Consistency is the key. I employ an ask, tell and demand system. I repeat the command, when necessary, until the dog understands what is expected of him. After that, if the command is given it is first an ask.... I say the command and wait for the appropriate response. If the response is not given, I repeat the command, firmer, and may direct the dog to comply i.e. for a "sit" command, push on their butt. If the command is still ignored I will demand compliance. Repeat command firmly, correct dog for the wrong behavior and MAKE dog comply.
I wouldn't worry about your dog being a biter unless you let the behaviour go without correction.