Please have your pup checked by the vet. A puppy/dog should stop peeing as soon as you pick him up, so that could indicate a problem right there. Also a puppy that age will probably need to pee after all naps, first thing in the morning, after playing, eating and shortly after drinking. Withholding to much water could cause a problem with UTI's. Ice cubes in a bowl ,at night or extended crate time,is a better way to limit their water intake without having the dog go thirsty.
He could be doing these things because he is nervous, however I would still have a culture done on his urine and have him examined.
No water while he's crated. I take him directly outside every time he comes out of his crate. I go with him outside every time, use keywords ("outside" "good potty") and reward him with treats when he's successful. Another thing is that even when I catch him in the act inside, say NO!/clap, etc, and pick him up to take him to his spot, he continues to pee (all over himself and me!).
He should not have to go that often. You should take a urine sample to your Vet and have it checked. He may have a stone or a urinary tract infection. He shouldn't have to go more than 3 times daily at 4 months of age. You don't want him to be holding his bowels too long either. It can cause other problems.
If he is drinking too much water he needs to be examined for that as well unless you are giving him too much. Are you giving him water while he is crated?