You could write a book about either one of your questions, there are so many what ifs and conditions involved. We are all unique. What works for one person may not work for another.
When can chick take the outside temperatures? What are your outside temperatures, especially your lows? Can they get out of a direct breeze and still have good ventilation? Have they been acclimated to colder temperatures?
My 3’x6’ brooder is in the coop. The chicks go in there straight from the incubator, even when the outside temperature is below freezing. I only heat one end but keep that end pretty toasty. There have been mornings ice was on the far end. The chicks stay where they are comfortable. Initially that’s almost exclusively on the warm end but as they age they play more on the far end, just going back to the heat when they need to warm up. My chicks are acclimated to colder temperatures which helps them feather out faster and they are better able to handle the cold. They also have great ventilation overhead but good draft protection on the level where they are.
If the lows are in the 40’s I generally turn the heat off by five weeks of age. One particularly hot summer I turned daytime heat off at two days and nighttime heat off at five days. By their body language they were telling me they did not need it and they didn’t. It’s not just that each of us are unique, each time brooding is unique.
When can chicks integrate with adults? Guess what, there is no set answer for that either. I’ve seen a broody hen wean her chicks at 3 weeks, leaving them on their own to make their way with the flock. But she had spent three weeks teaching the other hens to leave her chicks alone. She took care of integration. The other chickens had accepted the chicks as members of the flock. Those chicks still had pecking order issues. Older chickens outrank immature chicks and can enforce those rights, so the chicks quickly learn to avoid the adults when they can. In my flock it is really rare for a hen to even threaten a chick, I’ve never seen a dominant rooster do that, but occasionally you get a real brute that will go out of her way to be a bully.
With my brooder in the coop, the chick are raised where the flock can see them and get used to them. Since the rooster sees them as baby chicks he assumes they are his and has a protective instinct for them. By the time I let them mingle, they are accepted members of the flock, though they still have pecking order issues they will have to handle. If you introduce them without a break in period, they may be seen as intruders and may be attacked. Maybe, maybe not. But it is a good idea to house them with the adults for a week or more behind a fence so the adults can see them but not get to them.
One way chickens have learned to live together in a flock is that when there is conflict the weaker runs away from the stronger. It’s imperative that they be able to run away and get away, even with a little chasing. The more room you have the better. The chicks normally learn to form a separate flock and stay away from the adults as much as possible until they mature enough to force their way into the pecking order.
I’m raising 19 chicks right now. When the minimum temperatures hit the 40’s I moved 12 of them to an unheated grow-out coop but left 7 in that brooder for my own reasons. They were just over five weeks old. The next day, at about 5-1/2 weeks old, I opened that brooder door and let the chicks mingle with the adults. No problems at all, but I have a lot of room. I’ll let the other 12 out to mingle when they learn to sleep in the grow-out coop instead of on the run floor. My run is 12’ x 32’ plus I have about 45’ x 90’ in electric netting. This particular brood is not as afraid of the adults as many are. Each brood is unique.
Not everyone can do this. If you don’t have sufficient room, if you cannot get them used to each other before you let them mingle (or sometimes even if you can), or if you happen to have a brute in your flock you might need to wait until the chicks are practically grown to be able to successfully integrate them. Even then there could be some fairly severe pecking order fights, especially if room is tight.
One of the things you can do to help reduce integration stress is to create room, even if room is tight. Put things in the coop and run so the chicks can hide behind it or under it. Some perches high enough that the chicks can use them to get away from the adults can help. Provide different feeding and watering stations so the chicks can eat and drink without having to challenge the adults. A safe haven can help, a space with an opening big enough so the chicks can get in but the adults cannot follow. Housing them side by side for at least a week can really help, but it does to solve all problems.
Chickens are living animals. You cannot predict with accuracy how any chicken will behave, but I really think the most important aspect of integration is how much room they have.
I warned you it would be two books. Good luck!