With 8 bantams you should be fine with a coop and run those sizes.
Integrating those chicks may be real easy and it may be real hard. There is always a risk involved with any integration, even if they are the same age and size. Sometimes it goes so well you wonder what all the worry was about, but occasionally it is a disaster. It practically always involves some pecking. You never know for sure how it will go.
A broody hen does not wait until they are all the same size as the other chickens in the flock to wean her chicks, but the smaller they are and the more difference in size, the greater the chance that something bad can happen. A three week old chick is a lot more advanced than a day old chick.
You have two basic types of aggression to worry about. One I’ll call integration. Chickens can recognize which chickens belong in the flock. Sometimes they will be pretty aggressive about defending their flock and territory from newcomers. Sometimes they welcome them into the flock. But this is where housing them side by side where they can see each other but not get at each other can be so helpful. They at least recognize the other’s right to exist in the neighborhood.
The other problem you will almost definitely see is the pecking order. Like a herd of cattle or a pack of wolves, chickens are social animals. Each animal in the flock, herd, or pack needs to know its social rank so they can live together peacefully. But sometimes determining this rank can involve violence. This is natural and normal. You can’t get upset at every peck you see.
What will normally happen with chickens, the higher rank will peck the lower rank if they invade their personal space and the lower rank will run away. Order has been established and preserved. If the lower rank does not run away, this is a challenge to the pecking order and can get pretty violent. So space is really important. They need enough space to run away. After the pecking order is established these perceived challenges really drop, but with chickens of different maturity levels, the older is real prone to peck the young if they get close. That’s why you usually see two different flocks when you have two different age groups. The younger try to avoid the older as much as they can. It is less painful that way.
Occasionally you will have a chicken that is really aggressive and will actively pursue the younger to do real harm, even if you have plenty of space. This type of chicken is really rare in my experience if they have room, but they do exist. I have trouble emphasizing how important it is for them to have enough space.
With your specific situation, I’d suggest you divine your coop or brooder into two sections. As long as your coop gives good draft protection and you have electricity for a heat source, this could all be in the coop. You don’t have to keep the entire brooder or coop the perfect temperature for their age. All you need to do is to provide one warm area for them to go to when they need it and let the rest cool down as it will. One heat source where the brooders meet works great. They will find their own comfort level as long as they have room to get away from the heat source if it is too warm.
Leave them separate until you think the younger ones could use the run. That means they are fully feathered out, usually by the time they are 5 weeks old. Hopefully the older ones will have been using the run. Then remove the barrier. Personally I’d do this in the morning when I will be around all day to check in on them. If you try it at night, be very sure that you are out there before they wake up to open that pop door so they have more room to get away from each other when they wake up. The biggest danger is that a young one gets trapped where it cannot run away. The others might kill it then.
Have different feeding and watering stations inside and out so they can eat and drink without having to challenge the older chicks. And put some things in there they can hide behind or under, kind of out of sight, out of mind.
You are dealing with living animals so I can’t give you any guarantees. I think you have a pretty good chance of things working out well. Good luck!!!