I guess it depends on the weather but I don't usually keep my chicks under heat for more than a couple of weeks, even in the depths of winter. I find that they feather out much quicker if I generally reduce the heat in the brooder and then take it away completely. At 4 weeks I normally have my chicks outside in a 1 metre by 2 metre brooder. It has a roof for the rain and an old dog kennel for further protection attached to the back. I wouldn't put 4 week chicks in with a flock. They will only get picked on and in the worst case killed.
If your coop is empty then you could move them in now. If it has been previously occupied, it will need a good clean of course.
But if you have the means to put them in with the flock but separate them somehow then i think it is ok to do so.
I move my brooder in with the flock around this time so that they can get used to one another and the brooder gives them the protection they need.
In terms of milestones, chicks at 4 weeks should really be behaving like adults in the sense that they eat, scratch, take dust baths, etc. My 4 week old chicks move onto normal adult feed around this time. I start them on feed specifically for chicks (mash) and will slowly add grains to the mix until I get an adult mix.
The first few weeks of life are the most amazing, watching chicks grow is always a great entertainment, especially watching the different colours emerge in the plumage. There is nothing more to do now than sit back and relax and watch the friuts of your work.
