Here are a few thoughts, but I cannot give you a definite answer:
According to Halifax Humane Society a dog should drink about 0.5 - 1 ounces of water per 1 pound of body weight.
If your dog is 11 pounds, he should drink 5.5 - 11 ounces of water.
If the water bowl holds 1/6 cup, he drinks 6 - 10 ounces of water.
If the water bowl holds 1/4 cup, he drinks 10 - 16 ounces of water.
You see that a tiny difference (is it 1/6 of a cup or 1/4?) can add up. WebMD agrees that a 10 pounds dog should drink a bit over one cup a day. If he truely drinks more than 11 or 12 ounces, you should get him checked by a vet. Tell the vet that he drinks more water than usual, the vet will then looks for symptoms of different illnesses like diabetes, cushings disease or others.
Dogs have a very fine nose and can smell things humans cannot. That means he can smell that the places where he peed in the past still smell of urine. What ususally smells of urine? The toilet.
As long as the smell is still there, he might think that this is actually the right place to pee. There are special cleaners and detergents with enzymes that destroy the chemicals that smell like pee. Clean all the surfaces and carpets where he peed in the past with such an enzyme cleaner. Since urine glows in UV light, you can find his old spots with a UV flashlight.
At 2 years he's now a dog-teenager, and he acts accordingly. Maybe he wants to be the strong man in the family, maybe he wants to be a bad boy, maybe he just doesn't care. What he needs now is very strict rules, a strict daily schedule (or maybe a ritual) and probably some manners.
Go out to let him pee at the same time every day. Teach him a new command like "go potty" by saying it every time he pees. When you catch him soiling the house, tell him "No!" in a stern voice, but no more than that (don't talk to him). Then immediately go outside with him (it's best to grab him by the collar so he cannot run away) and tell him to "go potty" outside. When he does pee outside, tell him how good he is with a very happy voice.
You could also try not allowing him to sit on the bed. In dog language, the one who sits on the highest spot is the highest ranking dog. By not allowing him on the bed, you tell him that he's not the boss here and isn't allowed to do as he pleases.
Another reason might be that he's marking his territory. Desexig him (castrating or sterializing) might solve the problem, but there is no guarantee that it suddenly vanishes. You'll probably have to teach him that he's not allowed to pee in the house nontheless.
Personally, I would always desex male dogs, because they become slightly less dominant and more balanced. Their natural mating instinct causes them some stress every spring. In my personal oppinion a one-time medical procedure is less stressful than feeling the need to find a mate every year and not having the chance to find one.
I might have gotten the wrong impression, but it reads like the dog spends all his time in your room and your parents don't really interact much with him. He's also banned from carpeted rooms, which I assume are the rooms you or your parents spend most of your time in.
If this is the case, you could try a very different approach: supervise him at all times. You can put him on a leash and fasten the other end onto your belt loop. That way he's always close by and can be in rooms where he wasn't allowed, but you can always have an eye on him. If he makes a move to pee, tell him immediately "No!" and go out with him to pee.
Don't rub it in
Some people think that if they scold the dog in front of his puddle of pee or even push his face into the puddle, the dog will understand that he shouldn't pee in the house. This is completely wrong and doesn't work at all. Please don't even start this.
If you catch him right in the act of peeing, this is the only time scolding him will be effective. When he's finished and you find the puddle, no amout of scolding will change a thing. Dogs cannot connect the result of an action (puddle of pee) with their own past action (peeing in the house). So you must scold him for the action, not for the result.