Hi Pixie
I don't know how you have your place set up but I have a small chicken house integral with a run, completely enclosed, so I use that for any new introductions, put within the main chickens' area.
It gives the new ones grass to eat and scratch in, they can see out and the rest of the flock can see them but they can also go upstairs into the house if they want to be apart. The hens normally come over, wander round a bit to see what's new, then go off again. occasionally there's a hen fight through the mesh but it's better than face to face on their first day.
This has worked really well with my recent broody, I moved the nest in there, and the chicks all grew up in there. I put my cockerel in there on his own when he first arrived, although it was a bit small for him, so I only did it for a day or two. I also reared my first goslings in there, lifting them into the house part at night, same with the ducklings I have in there now.
It's a good way of separating a poorly one as well, without them leaving the flock and the problems that can cause reintroducing.
You have to gauge it for yourself but you can tell when the chicks want to explore further, and the mum will definitely appreciate the space. I have divided up the chicken run as a whole into three separate areas. This means new ones can have one part while the rest of the chooks have another. They are separated by 4' high mesh attached to posts/rails so they can all see through it and some of my hens fly over on their travels. They can then mix gradually.
As I've said in a different post, it's important to make sure everyone gets their own food so with this set up the chicks eat inside the run, the hens eat outside and when everyone's finished I take all the feeders away and then open the doors for them to mix.
I have had no qualms in putting very young chicks/ducklings/goslings outside during the day when we've had warm weather, with plenty of shade and water available etc the goslings came on so fast. They go in that house I mentioned already or a little triangular thing meant for a couple of small chickens in a garden. It's a bit of a performance rounding them all up morning and night but they enjoy the fresh air and scenery so I don't mind!
I'm not an expert on poo, but red can be the lining of the intestines which they naturally shed from time to time. There's a page on this forum with pictures to help you identify!
With the young cockerel it depends what you're going to do with him. I guess he can stay with his sisters until he shows an interest in them, then he would need to be separated, but if you can find a home for him sooner then do that. If he's destined for the pot he'll need to be separated and fed differently anyway.
Hope that helps, Good luck with all the babies!