The peeing is either excitement or he's showing submission. DO NOT YELL OR CORRECT HIIM FOR THIS. Try ignoring him for 5 or ten minutes, then calming saying hello and petting if he's calm.
As for the biting, I think he's playing landshark.
It's completely normal, and the fact that he only does it to you and your family means he wants to play with you.
Expecting a 4 month old pup to lay quietly (until he's completely worn out) is like expecting a two year old to amuse themselves the entire day by themselves. Seriously. He needs constant supervision, and direction to appropriate outlets (Toys, kongs or chews) and crate training so he can be in the crate with a kong if you're not available. Does he have a crate? GET ONE AND LEARN TO USE IT. It will save you.
Also and last: he needs EXERCISE. And LOTS of it. At 4 months I could walk my pup at least two miles. Sometimes not all at once, but definitely at least that much a day, if not more. Off leash hikes, if you're lucky enough to be able to do that REALLY tire a pup out. And teach him to be by your side, too. Keep your training sessions short, 3-8 mins and do them several times a day. When ever you see him doing something you want, praise and treat him. But EXERCISE, EXERCISE, EXERCISE.
Oh, and did I mention exercise?
Posted at the same time as Sharkey, and I missed the popping on the nose.
Please--I have never, in 20 years ever had to resort to hitting any of my dogs. He's just a pup. Get some Ian Dunbar puppy books and read them.