Hi and welcome to YT. Congrats on your new little one.
In my opinion, you little guy is way too young to limit foods and water. At 11 weeks, he should be being fed at least 4x a day if not free feeding. His blood sugar can drop very quickly--especially at 2 lbs. You have to visualize the size of his stomach and think about just how much food he can eat at one time, not a whole lot at all. His little stomach is probably the size of a dime.
As for water, you should have water available at all times. I never like restricting water, I even put one of those rabbit water bottles on Hot Rod's crate.
At 11 weeks, the best tip that I can give you for successful potty training is patience, patience, and more patience.

Keep in mind, his little bladder and how much fluids he can keep in him. Can you take him out every hour? For sure every 2 hours. Remember, puppies do not automatically know that they are supposed to potty outside or on a potty pad,they need to be taught/trained. Their mothers stimulated them to potty and they did so whenever and wherever.
Diligence on your part, you need to figure out his signs as to when he needs to potty. Look for anything that will give an indication that he is restless and walking in circles, etc. At this point, you should take him out or put him on a pad. Once he is in the actual act of pooing or peeing, say a phrase for that purpose. Then praise profusely. Treat also. This phrase should only be used when you take him out to potty. I use "do your stuff" and mine know what this means. We kept them on potty pads as we boat so we wanted to make sure that they would use them. They are pretty regular in that I know when they will poo. They usually do it 2x a day, on our first walk and then after work. If I come home at lunch to walk them, Hot Rod will usually go then, as I don't get home until 2- 2:30. Maggie will usually be after work.
We also got an expen for Hot Rod. I had his crate, potty pad, food, water, and toys in there. This way if we were delayed in getting home, he had all he needed.
As for his not wanting to be in the crate, I can certainly understand that, but you will need to be strong. Do you exercise your pup? By playing or walking him, you will tucker him out and come bedtime, hopefully he will be tired.
something that I started with Hot Rod: I put a regular bed pillow on my lap, turned down the family room lights and told Hot Rod, "nite-nite". He would grab his lamb that we got for him the very first weekend we had him, and gnaw on his tail until he literally fell asleep with it in his mouth. lol He is 2 1/2 years old and we still have this ritual. I just love this time as it gives me time to stroke them and just cuddle with them.
We also put them in their pen at night and we go up to bed. They know that when we get up, it's time for them to go into the pen. Whether they are asleep on the pillow/sofa or playing, when we say "nite-nite" they go into the pen willingly and go into their beds. Again, we have a potty pad in their. We've since taken their food and water out of there. Sometimes, if they have been gnawing on the bullies, I will put water in for them.
Sorry this is so long, but this is what has worked and works for us. Hope this helps somewhat. Here is a picture of our pen. Best of luck to you. Patience...it will happen one day.