I don't know where you are located so I have no idea what your temperatures are going to be the next week or two. Most chicks fully feather out by four to five weeks old so they can handle most weather then, I've had broody hens wean chicks at 3 weeks old and totally leave them on their own to make their own way with the flock. That was in warm weather with nighttime lows in the 70's Fahrenheit, three-week-olds could easily handle that.
Those broody hen raised them with the flock and spent three weeks teaching the others to leave them alone. I do like my broody hens. I also had a lot of room inside the coop and outside, plus weather that they could all be outside all day every day. You did not raise them with the flock and your coop is tiny, that's probably not going to work that easily for you.
My brooder is in the coop, the chicks go straight in there from the incubator or post office. When they are five weeks old I open the brooder up and let them roam with the adults. It's that easy. But you don't have that much room and yours were not raised with the others. You have to be a lot more careful.
When a young chick invades the personal space of a mature hen, or even just a more mature chicken, it is likely to get pecked. It usually doesn't take the chick long to learn to stay away from those older bullies. They need enough room to get away from the older ones if they get too close and they need enough room to avoid the older ones to start with. Your coop does not have that, I don't know how much area you have outside or if they can have access to that.
Chickens don't like change. A big change is strangers showing up. If you can house them across wire so they can get used to each other you can help a lot. This does not solve all your problems but it greatly increases your chances for success.
My first suggestion is to finish that larger coop as soon as you can. In the meantime, house those chicks where they can be seen by the older ones. When you do try to put them together give them as much room as you can. Provide widely spread out food and water stations, hopefully you have enough room. You might be a good candidate for the safe haven method. That's where you provide holes where the littles can get through but the older ones can't. I'd wait at least a week with them side by side before I tried that.
I can't tell for sure but it looks like you might be using that clamp with the heat lamp. If you even need that heat lamp, I strongly suggest you get rid of that clamp and use wire or chain to support it. Do not use string or plastic that can burn or melt, use wire or chain so it cannot be knocked down. That will greatly reduce your fire risks.
Those broody hen raised them with the flock and spent three weeks teaching the others to leave them alone. I do like my broody hens. I also had a lot of room inside the coop and outside, plus weather that they could all be outside all day every day. You did not raise them with the flock and your coop is tiny, that's probably not going to work that easily for you.
My brooder is in the coop, the chicks go straight in there from the incubator or post office. When they are five weeks old I open the brooder up and let them roam with the adults. It's that easy. But you don't have that much room and yours were not raised with the others. You have to be a lot more careful.
When a young chick invades the personal space of a mature hen, or even just a more mature chicken, it is likely to get pecked. It usually doesn't take the chick long to learn to stay away from those older bullies. They need enough room to get away from the older ones if they get too close and they need enough room to avoid the older ones to start with. Your coop does not have that, I don't know how much area you have outside or if they can have access to that.
Chickens don't like change. A big change is strangers showing up. If you can house them across wire so they can get used to each other you can help a lot. This does not solve all your problems but it greatly increases your chances for success.
My first suggestion is to finish that larger coop as soon as you can. In the meantime, house those chicks where they can be seen by the older ones. When you do try to put them together give them as much room as you can. Provide widely spread out food and water stations, hopefully you have enough room. You might be a good candidate for the safe haven method. That's where you provide holes where the littles can get through but the older ones can't. I'd wait at least a week with them side by side before I tried that.
I can't tell for sure but it looks like you might be using that clamp with the heat lamp. If you even need that heat lamp, I strongly suggest you get rid of that clamp and use wire or chain to support it. Do not use string or plastic that can burn or melt, use wire or chain so it cannot be knocked down. That will greatly reduce your fire risks.