Your puppy is very young and his training will take time, consistency, and patience. It is quite the accomplishment that your puppy is already learning to pee on pee pads. You should schedule a potty time & stick with how often you take your puppy out. He should be taken to go pee every couple of hours. Try and keep track of when he goes #2 and try to get him to the area you want him to potty at during this time. Praise him immensely when he does do things right and reward him. He has a very tiny bladder at this time, and doesn't quite understand where you want him to go potty yet. Everything will take time, but can be accomplished. You might have to start waking up in the early morning to let him out to potty in the appropriate area. Even though your puppy doesn't have shots, if you designate a spot in your yard for your puppy to go potty and don't let him explore anywhere else he should be fine (just make sure no other dogs go there) or you can continue to use the potty pads. As for crying at night, try making an x-pen in your room are sleeping with his crate near you?? Maybe start letting him sleep in your bed?? His crying will get better with time.
Owning a puppy is a lot of work. It requires much time and patience. Puppies, like any other babies, have to learn how to do everything and have repetition to remember what it is you want them to do.
I hope that you can find a way to deal with everything through your frustration. I know puppies can be a handful. I do sympathize with you, but please understand that your puppy doesn't actually know right from wrong at this age. It is up to you to teach them everything that you want them to know. Your puppy is bound to make plenty of mistakes throughout the first year of life. It is a learning experience for both of you, really
Patience, Repetition (Positive Reinforcement), Time, and Consistency are KEY when training a puppy.