Thanks for the details, this REALLY helps. As I mentioned, I'm in the process of an integration myself. So I'm trying to learn everything I can. As it turns out, mine "integrated" earlier than I had intended. I go out to the coop yesterday afternoon and all 16 chicks (6 new and 10 existing) are in the coop together in the same area. I'd left the new chicks free to run around inside the entire coop (not confined to their penned in area inside the coop). I accidentally left the pop door unlatched and it must have popped open. All 10 of the older chicks had gone in. So... effectively, the chicks were integrated. I watched them and it was just as you said, Percheron Chick, the bigger chicks chase the younger ones and the younger ones scurry out of the way. So far... (crossing my fingers) there has been no blood, no pulled out feathers, just a bit of squawking.
Could have been a big mistake, leaving the pop door unlatched. I'm glad it turned out OK (again, so far, not counting my chicks until...) I'm glad I did it this way too, confining the new chicks in the coop safely behind the fence but with the older ones. I left up the fencing but it's open. So now, the younger chicks run in there to be separate whenever the big chicks come in. The 6 new ones also sleep on the picnic bench seat I put in there, just like they have this whole past week when they were confined to their little area. They have a separate food and waterer in their little area too, so that helps them not compete for resources. Finally, there are many places to hide in the coop when they get caught outside their little fenced in area. For example, I have 2 hardware cloth covered "screen" doors which swing into the coop. I keep these wide open and they each provide yet another area that the little chicks seem to hide behind quite a bit.
What your experience tells me is that I'm not out of the woods yet. I know it takes 2-3 weeks for the integration to really be done. I need to keep a really close eye on them until then. I've also been getting up with the sun to open up the coop and let them out to free range so they're confined together as little as possible. And I supervise them going to bed each night. I'll do this until the little ones get up on the roost on their own and safely without being overly (more than the normal amount of bickering and jockeying for position) abused on the roost.
Anyway... back to your questions. In terms of a hen going broody, do a few searches on this in this website and there is tons of info on this. I also want to have a broody but I've got time to figure this out so don't know much about this. I have read some and I do NOT think you need a separate coop for your broody hen. However, I don't know how big your coop is or how it's set up so I can't say for sure.
I don't think that what happened to you necessarily signals that your other 2 12 week old chicks are roosters. As I understand it from all my reading, roosters are not mature enough at that age to command much respect from full grown hens. In fact, full grown hens will often (always??) be higher in the pecking order than younger roosters. They could be roosters and were able to defend themselves better than the pullet that was injured and then killed. It's hard to say. Can you post pictures of your 2 remaining 12 week old chicks? I (and others) can gladly try to tell you what sex they are. I'm getting pretty good at it and by 12 weeks of age, it's often easy to tell with many breeds. I don't think you ever said what breeds they are but post some pics and we can give it a shot.
Hope this helps,
Guppy