First, congrats on the puppy!! He's super cute!
Second, I am by no means an expert, but as far as the housebreaking goes, it sounds like you're doing alright. We had a relatively painless time housebreaking our dog, and it sounds like you're pretty much on the same page that we were. It just took time, but if you're consistent, they catch on pretty quickly.
You just have to keep taking him out, praising him when he goes outside, etc. We used the phrase "On the grass" and praised him when he did his business, and now he goes on command for both #1 and #2 with that. It comes in handy for when I know he hasn't gone yet and I need to leave the house!
He also scratches the door when he wants out, which was helpful when he, and thus his bladder, were smaller. Now he scratches when he wants to go out and sun himself or chase rabbits.
Also try to recognise his "I'm gonna go" behaviours. We eventually could tell when our dog was going to do #2 because he would start sniffing around in a circle with his tail straight up in the air. My first dog ever would bolt for the end of the hallway as that was his spot, for some reason.
Eventually you'll get to know what his schedule is like. For example, ours just never wants to do #2 first thing in the morning, even though he's been sleeping for 9 hours. It's pee, breakfast, back to sleep for 30min - 1 hour (him, not us, the lazy bum!
), and then a poo around 7:30. Then it's another 1 or 2 in the afternoon and one before bed.
As for the screaming. I have very little advice. We were complete wimps. I think you just have to get through it, which I believe is what my parents did with our first dog. Perhaps put something cuddly in with him, as well as something that smells like you. It might comfort him?? Also, it could also partly be that the kitchen is too big a space for him, and closing the door to the crate might actually help. Smaller spaces tend to feel safer to dogs, so he might find it easier to settle down if he doesn't have such a big space to be alone in.
We tried to leave ours downstairs in his crate the first night. Oh the screaming! We couldn't handle it, so we moved his crate up to our bedroom and just lay next to the crate for a few minutes until he settled down. He'd then proceed to snooze, and we could snooze. He'd get up a few more times and we would just go comfort him again, but after the first week or 2, the screaming had stopped. We just kept him in our room at night after that, until he was old enough to be trusted out of his crate at bedtime, which is when he starting sleeping with the kiddo instead. We'd always intended to have him sleep in the kiddo's room anyway, so we didn't really feel that it was necessary to keep him downstairs at first as originally planned.
And now I've gone and rambled on and written my life story! I hope some of that helps, at least a little. Good luck!