Welcome to the forum!
Glad you joined us!
We all have to start from somewhere. Don't feel bad about not knowing about breeding or hatching. And expect to get a lot of conflicting advice on this forum. We all have different goals, different circumstances, and different experiences. We are dealing with living animals, each with distinct personalities. There is seldom one answer that fits all of us.
I don't know how old your younger flock is. Some roosters start crowing at a very few weeks and some wait a few months. Some of us do not mix young chickens with adults until the young ones are fully grown. Some of us do it when they are really young. There are different reasons for that, but a lot depends on what experiences you have had and how much space you have. Each flock is different. If yours are already living together with no bloodshed, I would not change anything. You've made it through integration, which is sometimes a pretty peaceful process but sometimes a process where chickens wind up dead. It's one many of us dread but which usually works out.
You could write books about your questions. When the roosters mature, they will mate with all the hens. Any of the hens may lay fertile eggs. If that is the concern about separating the flocks, don't worry about that. If you have another reason to be concerned about separating the flock, please let me know what that reason is. Until a younger rooster matures enough, older hens may beat him up unmercifully, but again, they may not. They are living animals. Who knows what they will do? We have had a lot of different experiences with that.
Not all hens will go broody. Broody means they want to hatch eggs. Whether a rooster is around has nothing to do with whether they go broody. A rooster just has to do with whether the eggs are fertile. When the hormones kick in, they go broody and will set on a nest and try to hatch eggs. It doesn't matter if there are any eggs in the nest or not. When the hormones kick in, they will set on their imagination.
Does time of year matter? Some. More hens will go broody during the spring and summer than the fall and winter. But several of us have had hens go broody and raise chicks with snow on the ground.
I know. Short answers to some pretty complicated questions. But hopefully they will help you some. And once again,