Most of this is down to training.
By 16 weeks, the average Golden Retriever should be able to walk to heel off lead, be fully house trained, and understand most societal norms. Training should be done around every meal - don't just stick a food bowl down and let them have at it. Use meal times as a training opportunity. Reinforce that he sits and waits for food, for attention etc. They are incredibly intelligent dogs - more intelligent than their owners, the majority of the time - so training is a walk in the park, particularly given their food drive.
Your boy barks when he's shut in the pen because Golden Retrievers are social animals. They can suffer with severe separation anxiety. You cannot leave him in the play pen crying. Again, a firm no if he bothers you when you eat will fix this. As will giving him a small reward once you've finished eating - so he knows his reward comes after you have eaten. Eventually he'll lean to wait. But leaving him to cry will only end badly.
Finally, on the biting. He did not try and bite your 4 year old. He mouthed. Golden Retrievers mouth their entire lives. They can literally spend hours with something, the same thing, in their mouth. They were bred to have something in their mouth. You need to feed that desire - that means toys, pillows, towels (all supervised) whilst your puppy goes through teething and gets used to understanding the force of it's bite. The mouthing will go on your dogs entire life - you need to get used to that because in six months, you'll have a 30kg dog that still mouths and no amount of training will fix that because it's inherent in the bred.
Most of all, your puppy needs time alone with just the adults - without the child around. Children wind up puppies something chronic and, being honest, it'll be much easier to fix some of these behaviours if you keep your child and the puppy away from each other as much as possible.
But, what I will say, is this is going to be 2+ years of work. Most Golden Retrievers, even if they are well-trained and 'calm' still have wanky moments daily when they're 2-3 years old. It's why effective training - not puppy training classes which are a complete waste of time - is so important.
I would be careful upping the walking. I always tell owners of my puppies not to pay attention to the five minute rule - but to be mindful of their dog. Just because a dog can walk that far, doesn't mean it should. And walking your dog so it sleeps is not a long-term solution. Neither is using a kong or a puzzle mat. Puppies need to learn to settle, and be calm, and not bother people- and that's only learnt through experience, training and age. No one ever got a good dog by neglecting training and using Kong's or over-exercise to solve all their issues - but they did through training. 😊