once again, how do you not allow it?

I accidentally pulled out Trillie's center (longest) tail feather when I was helping him to go to sleep. Shame on me. Is it not a problem, will it grow back? He looks funny without it.

Maybe in time

thanks. But it doesn't hurt the bird in any way, I hope?

If it came out that easily, it sounds like it was ready to molt out. Even if it were forcefully pulled out, like say if you had to pull it out because it was a broken blood feather, it will come back. If it's pulled out by force like that, I think there's a small chance there could be a bit of damage to the follicle and the feather may not come back or it may come back funky, but I think that's low and only an issue if it's pulled out repeatedly.

Well, I grabbed him, and I guess held him at little tighter than normally (not often, but sometimes I have to grab some birds). I myself didn't expect it to happen but it was too late - it already happened. He seems to be all right. No changes in behavior.

The little ones start looking super skinny but they proudly turn their beaks away from my food (not all of them, thankfully). Just amazing. I don't see any other way out in this situation. I even don't weight them anymore - they weigh what they weigh and nothing will change if I know how little they weight. They have plenty of forces to be escaping from me though.
I do what I can, we went thru the same with the first clutch. Everybody survived and grew up all right.

Birds have the ability to release their tail feathers, to help them escape from a predator that has grabbed them by the tail. This may have happened with Trillie - you accidentally pulled on his tail feather a little bit so he let go of it. It will start growing back immediately.

I prevent my brother-sister pair from breeding using long nights. I made a nice thick cover for the cage that lets very little light through. I put them to bed at sunset and put this cover on the cage, and "morning" comes when I want it to.

do you do it to them all year around? I am a little cautious about thick covers, do they let air circulate enough?

I use thick covers and have never had a problem. If anything, I think it keeps him warmer, since his bedtime cage is in a cold spot during winter time. I don't tuck it in all tight around the bottom, I just drape it over the entire cage.

what should I do if Cuddles lays an egg?
In the past, she always laid an egg some time after mating (hasn't learned to mate for pleasure I guess). I don't expect this time to be different. I also don't think she would find unsafe that the box is appearing and disappearing. She is just this type of a hen. She has been mating for 3 days now, first thing in the morning - surrounded by her children who watch them.... (not a moral character at all
Of course, we wouldn't help her be comfortable with her eggs.
What is the right thing to do if she has an egg in the box? What to do if she lay an egg out of the box? We want her to lay as little as possible and not have any hopes about them.

I tried different covers on the cages. They didn't make any sounds until I uncovered them. The problem is that my schedule is not easy to match with the birds needs. I am not always home when they need to be put to sleep. DOn't get me wrong, I am back by 9 usually but if I am needed here for them earlier, it may not be possible.
You mentioned sunset, which ls 6pm here. Is it how early your birds go to sleep?

I don't use hormone control techniques all year long, just during the part of the year when hormones are a problem, which is roughly January through July.

It doesn't have to be pitch black inside the cage, just dark enough to seem like night. Wild birds sleep with moonlight so a small amount of light is OK. My cover is thick enough that when I drape it over my own head and look at a bright light I don't see very much, but I usually hang it so some space around the bottom of the cage isn't covered and a small amount of light can enter that way. I want the birds to be able to see a little bit so they're less prone to night frights.

The usual advice for when a hen lays unwanted eggs is to let her keep them, but that advice frequently doesn't apply to a hen that's starting on a third clutch right after two clutches where she successfully raised a lot of babies. If you confiscate the egg and keep up the hormone control, she'll usually stop without laying a full clutch.