Sometimes the integration goes so well you wonder what all the worry was about. Sometimes chickens end up dead. There are no guarantees either way. Broodies will sometimes wean their chicks at 4 weeks old, though some go a lot longer. I usually integrate at 8 weeks. Age is important but it is not the only thing. Personality of your chickens and space are the two most important things in my opinion.
Some things I think you can do that can help. Put the brooder in the coop where they can see each other but cannot get to each other. Make sure the young ones cannot escape the brooder. If they do, that is bad! If they can see each other, they will come to accept each other as part of the flock. That does not solve all your problems, but it is a big help.
Have as much space as you can when you let them get together. I free range mine (no fences). I'm convinced that makes my method work for me. If you don't have a lot of space, it is harder. Give them as much room to get away from the older ones as you can. Put in things that they can hide behind and have perches so the young ones can get up away from the older ones. It is hard to do since they grow so fast, but if you can create a safe haven for the young ones that the older ones cannot get into, that will help.
Set up separate feeding and watering stations. You can avoid a lot of conflict if they don't have to eat or drink together. I currently have three feeding stations and four watering stations, and they all use all of them. The older ones tend to like the ones I set up for the young ones and the young ones like the older birds feeding areas. And they free range so they forage a lot.
I think it is good to have separate predator proof sleeping areas if you can manage it. Mine are most vicious when settling in for the night on the roosts. They are kind of forced into a small area and the hens lower in the pecking order are the most cruel. It is not always a problem, but sometimes it is.
It is not all gloom and doom. Many of us integrate all the time and usually do not lose any chickens. But the risk is there.
As for your last questions. When are they adult? That depends on the individual chicken. When are humans adult? I've seen kids in their early teens be very responsible and I've seen 50 year olds that never made it out of the pre-teen stage. Size is not as important as maturity. I've seen 15 week old chickens be accepted as adults by the flock. They are still pretty low in the pecking order but they are accepted. I've seen others months older that are still not accepted as mature chickens. On average, I'd guess that mine are probably "mature" enough to have their position in the pecking order pretty much worked out by around 21 to 23 weeks, but that can vary a lot. Since mine are integrated while still fairly young, I usually don't see a lot of that pecking order sorting out later. They seem to do most of it under the radar. And with your two different age groups, you can expect them to basically act like two different flocks. They will intermingle some but will often hang with their buddies, not with the other group.
When do they start to lay? It is somewhat breed dependent but it is also very heavily an independent thing. Full blooded sisters can start to lay months apart. I have a flock of mutts that are based on dual purpose breeds. If I have 10 pullets, I'll probably see my first egg around 18 to 20 weeks. I have had first egg at 16 weeks, but that is rare. With mine, usually about half are laying by 23 weeks or somewhere close. All are usually laying by 27 to 28 weeks, but occasionally one will go months later.
With a lot of these things there is no one correct answer. They are living animals and each is its own individual. Hope this helps! Good luck!