I probably agree with Illia about 95%. In my experience, if roosters grow up in the same flock, and that can be either as "brothers" or in a father-son relationship, they normally work out their major differences with little fighting. Sometimes you will get some that fight to the death, but that is fairly rare. Illia made a good point. Certain breeds, like Games, are more likely to fight to the death. So my disagreement is not that there are no worries, it is that there are usually no worries. I am also speaking of my set-up. Mine normally free range (no fences) so they have plenty of room to get out of each others way. I think that makes a lot of difference. There are times I leave them locked in the coop and run and they still get along OK, but they do usually have room to get their pecking order worked out.
I have seen roosters square off with their neck feathers stuck out when they are about 5 weeks old. I have seen pullets square off with roosters the same way at five weeks or so. I've seen 12 week old roosters square off that way with a mature hen. It is all about pecking order. They will establish that pecking order, usually without much fighting but not totally without fighting. I have yet to have any chicken seriously hurt in either a pecking order or dominance fight. Again, I usually give them a lot of room. I do not keep a bachelor pad either. They all run together, males and females.
You can get another round of fighting when the boys hit sexual maturity, but I usually don't see much of that. They just seem to work that out when they are pretty young. And when the boys get mature enough to challenge Dad, it cam sometimes get pretty serious, but again, I have not seen it all that bad. They usually figure out pretty quickly which one is going to win and the other runs away.
When do they get sexually active? It varies. I've seen some try to get active around 12 weeks, which is before they are ready to be processed. I've seen some not start until around 19 to 20 weeks, but I'd say most are interested by 15 weeks.
If they don't have room to work out their differences and run away, that might be different. I don't have experience with that.
Good luck! Hope this helps a bit.