I would just put his bed in the crate with a potty pad covering the rest of the area. If he is drinking water at night he is naturally going to have to pee a lot during the night. Maybe buy him a small bed instead of the blanket. He is less likely to pee in his bed. Watch for the Lee pads with an attracting agent already in them. They are so helpful with training.
He is still very young. It takes months of close watch and a strict routine to train a puppy. Small pups sometimes take longer. A pup 6 months old or older would not need the water at night but your guy is just a baby. Puppies have a muscle attached to the bladder that does not mature until they are around 16 weeks old. They can't hold back urine very well until that happens.
I have always set up regular intervals to take the puppy out rather than waiting for them to ask. They are creatures of habit really. Once the routine is learned the dog will start reminding you if you are late.
