A lot of good questions. I’m going to assign some homework.
First check out this thread about a broody hatch in Michigan in winter. It’s long but shows you some of the things you need to address. Winter hatches are possible but are more risky.
I hatch in an incubator in the house and brood chicks in the coop in winter. My hens don’t go broody in winter or I’d let them do more of the work. My overnight lows occasionally get below zero Fahrenheit (-18 C) but cannot compare to yours. You can hatch and brood chicks in winter but it is harder with more risks. I’d suggest you wait until later for an additional reason. You can hatch the small pullet eggs, but I get better hatch rates and better chick survival if I wait until the pullets have been laying a while. When pullets first start to lay they sometimes don’t get everything just right for a chick to develop and hatch, plus the pullet eggs are tiny. There is not enough nutrients in those tiny eggs for big strong healthy chicks to develop. I do hatch pullet eggs and sometimes do pretty well, but sometimes the results are really discouraging. If you can it’s best to wait.
As far as how much room you need, follow the link in my signature. I don’t give magic numbers, how much room you need is really variable depending on our own unique situation. But with your climate, your plan for broody hens, multiple roosters, and integration, more is definitely better. All those factors scream for more room.
Roosters are always a big question mark. People do keep multiple roosters with flocks the size you are talking about. There are no magic numbers as to hen-rooster ratio either. People with one rooster to over 20 hens ratio have the same problems as flocks with much worse ratios and numbers as far as fighting, over-breeding, bare backed hens, and all the potential problems. I find room has a lot to do with success and your room is tight for that, especially in your climate. It varies a lot by the rooster and the hens, but one young vigorous rooster should have no problems keeping 15 hens fertile. Some roosters have trouble keeping three or four hens fertile. You are dealing with individuals and they don’t come with guarantees. I always suggest you keep as few roosters as possible and still meet your goals. That’s not because you are guaranteed more problems with more roosters, you are not, but because the potential for problems goes up with each rooster. If I were in your situation I’d go with one rooster but there is something to be said for having a back-up. Just be prepared to make management decisions if it shows it is not working out. Have a plan.
Broody hens have been hatching and raising chicks with the flock for thousands of years without the help of humans, even before they were domesticated. They did not go extinct. Bad things can happen if they incubate and hatch with the flock. Bad things can happen if you isolate them. When you are dealing with living animals bad things can happen no matter what you do.
I’ve never had an adult rooster threaten a chick in any way. I have seen the dominant rooster help Mama take care of her babies, but not all roosters do that. Normally the other hens leave the chicks alone unless that chick leaves Mama’s protection and intrudes on the other adult hen’s personal space. One peck usually sends the chick running back to Mama, with the chick maybe learning that it is bad chicken etiquette to intrude on your betters. Mama generally ignores this. But if the hen starts to follow the chick or otherwise threaten it, Mama politely whips butt. I’ve never lost a chick to another flock member but I know other people have. Each chicken has its own personality, each flock its own dynamics. We can tell you what normally happens but there will be exceptions.
Whether the eggs are fertile or whether there is a rooster around has nothing to do with a hen going broody. Broody is a hormonal thing. Some hens are a lot more likely to go broody than others. Many never will. You certainly cannot control the timing of when a hen goes broody. If you want to control hatching eggs, get an incubator.
Most broody hens, once they kick into full broody mode, are in it for the long term. Sometimes hens will pretend to go broody but not really kick into full broody mode. Occasionally you will get one that quits before the eggs hatch but that is fairly rare. They are living animals, what can I say?
We all go about this differently. We all have unique set-ups, goals, and experiences. With this kind of stuff there is almost never one right way to do something where every other way is wrong. There are just a lot of different ways to be successful.