Your puppy does not instantly know that he is not supposed to go in his crate, you have to train him to the expected routine. Be sure to watch the potty training series of videos and click on the Forum and type "potty" in the search box to review other members questions and their answers. So far as going in the car this is not unusual and again there has to be a routine to making sure he potty's before the trip.
It is not impossible that there could be a urinary tract infection that is adding to the peeing problem, be sure to mention this to your vet at the next visit.