1) When will the roos begin to try mating, are there any signs that indicate they are getting ready or do they just one day start mounting hens?
They just start.
2) Will they attempt to mount hens that are not sexually mature, or do they know this and wait?
I have some trouble with defining sexually mature. They will try to mount pullets that are not ready to lay if that is your question.
3) If I rehome 2 roos and keep the top Roo, will a roo be too much for 3 hens?
This one can get pretty complicated. There are a whole lot of different factors involved and we all have different experiences. Some people report no problems keeping 3 roosters with two hens, while others have problems with 1 rooster and 18 hens. It depends on the personalities of the roosters and the personalities of the hens. Age and space is important. You are more likely to have problems while the rooster is an adolescent than when he matures. Same with the pullet's age. My regular advice is to keep as few roosters as possible and still meet your goals.
4) If I do keep 1 roo, and I let the new pullets outside with the flock at 4-5 weeks (depending on weather), will the roo try mating with the youngsters, or will he know to leave them alone?
He will not try to mate with them until they get older. That will not be your problem.
This one can also get complicated. Integration can be a dangerous time, but many of us do it successfully all the time. Many chickens are bullies. They strickly enforce the pecking order. The older ones will dominante the younger ones to the point the younger ones will probably be very afraid of the older ones. Any older chicken, whether hen or rooster, can be a danger to younger chicks. I've found my hens to be more of a danger than the rooster, but that may not be everybody's experience. I've had broodies get on the wrong side of a fence from their chicks and totally forget the concept of "gate" so she does not go get them. At different times when this happens, I've had a rooster go to where the chicks are and just lay down until the hen figures it out. He's there to keep an eye on the chicks. I've had two week old chicks leave their mama and go eat out of the feeder next to adult hens with no problems. I've also had that same situatuion where the adult hen pecked the chick to remind it that it is bad manners to eat with adults. I've got a pretty laid back flock and a pretty good rooster. Others have had the older chickens kill the young.
There are some tricks to improve your odds. House the young next to the adults for about a week before you try to mix them, where they can see each other but not get at each other. Have them sleep in separate places for a while. I find the most aggressive time for mine is bedtime if they are sharing a coop. Set up different eating and drinking places. The older ones will often keep the younger from eating and drinking if they can. Try to have a safe place for the young with a hole small enough that only they can get through. Something extremely important to me, give them as much space as you can so the young can get away from the old.
I'm not going to tell you that if you do this everything will defininitely be OK, but I think it will help your odds a lot.
Good luck!!!