For the middle of the night screaming, I think something is probably disturbing them. It could be headlights from a car flashing into the coop, yard lights going on, a neighbor coming home from a late night or even a predator stalking around, that you don't know about. A nosy cat, dog or raccoon could be skulking around at night and be gone by the time you get out there with a flashlight. They'd probably hear and see you coming to check. Birds don't like rodents scurrying around them at night, either, even if it's outside. They could hear some scratching at the coop from any of these animals. Even light pawing or a little rattling of a door or window could cause frightened screaming. Those would be my best guesses. I would try to figure out what is causing the disturbance and then see what you can do about it.
For the daytime noise, spoiled demanding chickens can make a lot of noise! They can have a real sense of entitlement! The things they are most fussy about seem to be getting out of the run and being fed their favorite treats. Now, some aren't big complainers, no matter what you do, but some are. Sounds like you have big complainers. If their sleep is being disturbed, I would think that would only make them fussier. You could try keeping to more of a schedule for them and see how that goes.
Chickens that never get out of their run don't usually complain to get out. Chickens that get out of the run at the same time every morning usually don't complain that much, because they have a routine. Chickens that often get out, but then don't get out, seem to complain the worst. It's the same sort of thing with treats. If they are used to getting treats every day and then they don't get them or they're late, they'll fuss!
Maybe try letting them out at the same time every day or try an automatic door, so they don't have to wait. Either of those should help with the screaming to get out. Do they have enough square footage in the coop and the run? Is the screaming for you to come out in the yard related to you giving treats? You could try stopping all treats or you could only give treats once a day, at the same time.
I would also check them over for external parasites, just to make sure they don't have any mites biting them. That makes chickens fussier, too. So can molting. Some breeds are just more high strung, too. Or one chicken can get the others going.
