Welcome to the forum, glad you joined.
You answered my question, why do you want roosters. You want fertilized eggs so yes you need a rooster. Now the question is how many.
There is no magic number. When you deal with living animals and their behaviors there are no absolute answers. Some roosters have trouble keeping more than 4 or 5 hens fertile. That is really rare and generally means the rooster is really old, there is something physically wrong with him, or he is so deficient in personality he cannot win the respect of the hens. I'll repeat, this is rare. With a young active rooster I would not expect this.
Most of the time when you keep one rooster with a flock of hens he can keep many hens fertile, provided he has access to them all. How you manage them can have an effect. You will often see a 10 to 1 ratio mentioned on here as if it is a magic ratio that solves all problems. it doesn't. That 10 to 1 for full-sized fowl and 12/15 to 1 for bantams are ratios that hatcheries have found will pretty much assure that all eggs are fertilized when they use the pen-breeding method. The pen-breeding method is when they keep maybe 20 roosters in a pen of 200 hens. Due to the dynamics of that method, the numbers of chickens, and the randomness of which hens get bred, it take that many roosters to assure practically all hens are laying fertile eggs. I don't think you are keeping them that way. You just don't have that many.
Dad kept one rooster with 25 to 30 hens in a totally free range situation. No fences to keep them in at all. Practically all eggs were fertile, even with roosters 4 to 5 years old. From a fertility aspect one rooster will probably suit you fine. Some people like to keep spares, I don't.
The other part of the question is social interaction. When they are immature cockerels and the pullets are still relatively immature it can get really rough down there. The cockerels' hormones are running wild, telling them to dominate. This means cockerels often have serious fights for flock domination.
It also means they harass the pullets because, at that age, the mating act is more about domination than sex. The one on bottom is accepting the dominance of the one on top, either willingly or by force. The pullets are still immature enough that they don't know enough to do their part and submit willingly or the cockerels have not yet won their respect. As a result it can get really violent down there, I think you are seeing that.
Eventually when the cockerels mature into mature males they gain control of the hormones and exhibit the qualities the now-mature pullets want in the fathers of their chicks. The flock turns really peaceful with males and females doing their part. At least this happens most of the time. Occasionally you get a male that never grows up or a female that will not accept the rooster's dominance. That's the unknown part of dealing with living animals.
I'm a firm believer that the more room you have the more likely you are to have a good result at any stage of this growing up process. That does not guarantee you won't see problems, you probably will when they are immature.
Another question is how well will two or more mature roosters get along in the same flock. Again, I think the more room you have the better your chances of a good result. What often happens is that when they mature to a certain point each rooster stakes out his own territory and keeps his own harem. If they can stay out of sight of each other there is generally little conflict. This is the ideal situation. That doesn't mean you can't keep two or even more in a smaller space, some people manage, just that your odds of success are better if you have a lot of room. But hatcheries using the pen breeding method keep many roosters in pens with a lot of hens so you certainly have a chance at success with less room.
I generally recommend that you keep as few males as you can and still meet your goals. That is not because you are guaranteed more problems with more roosters, but that problems are more likely. If room is tight the problems are much more likely. In your situation I'd only keep one. If you want a spare in case something happens to one, you can try keeping a second male with the flock, it might work out. Or you can build a second pen and house just one rooster by himself or give him his own harem. If you do try to keep two with the flock I'd have a Plan B ready, a separate enclosure where I could quickly put one of the males if the need arises.
Good luck however you decide.
