How do I know they are mating?

I have one black Cochin rooster and 49 hens. I have seen him mate with 3 of the hens and I suspect a 4th because she's losing feathers on her back. I'd like to eventually incubate and hatch my own eggs but how will I know he is mating with what chicken? Do I just have to separate the hen I want bred with and him from the rest of the flock? Can I assume he's mating with the whole flock? I'd like a different rooster, a breed known for better laying to mate with the hens but I can settle with the Cochin for now.

49 sounds like a lot for one roo to cover. I'd suggest separating him with maybe 10 girls. There's no way to know if an egg is fertilized without breaking or incubating it, but once you've had them cooped up in a smaller flock for a while, you can crack the eggs open to check for fertility. On the yolk, you should see a small bulls eye (a little smaller than a quarter inch), it's called the blastocyst.

One vigorous young active rooster can keep maybe 20 to 25 hens fertile without much problem. An older less vigorous rooster may have problems with just a handful of hens. It varies a lot by the rooster and the hens have a part to play too.

A rooster just has to mate with a hen about once every two weeks to keep her fertile. That’s why one rooster can manage so many hens. But with that many hens you are highly likely to find that a lot of eggs are not fertile. I suggest isolating him with about ten hens, then maybe a week later start collecting eggs to hatch. This shows what to look for when you open an egg to see if it is fertile. If most of the eggs you are opening are fertile, most of the eggs you are not opening are also fertile.

Fertile Egg Photos
https://www.backyardchickens.com/t/16008/how-to-tell-a-fertile-vs-infertile-egg-pictures

This is your chance to improve your overall flock. Carefully select which hens you put with him for these hatching eggs. Choose your breeders for the traits you want, whether color, body build, egg laying, temperament, whatever. I personally would not use the hens that are showing feather loss. Some feather loss is normal and natural during mating, but some hens have brittle feathers. Because of genetics the feathers can break really easily. Since you have one rooster with 49 hens it’s not very likely the rooster is doing anything seriously wrong. The fault is likely to be with the hen somehow, even if it is not brittle feathers but something else.

Ok, thanks!

That's why I'm thinking about getting a different rooster. The Cochin is cool to look at (I call him Elvis because he has black long feathers) but I want a better laying breed.

If I get a new rooster, can they co-exist together?

Many people have kept more than one rooster with a flock for thousands of years. If you check out some of Centrarchid’s posts he’s observed some remarkable things about roosters and he keeps a bunch. But one huge factor is how much room they have. If they have sufficient room where they can set up different harems and occupy different territories they can coexist. If they are constantly thrown together conflict is more likely.

It’s not a matter of so many square feet per chicken. Can they get far enough apart to avoid conflict? They may spend part of the day together. They can probably even sleep in the same coop as long as you don’t leave them locked in there very long after they wake up. They can and do coexist, sometimes in pretty small areas. But your chances of success are much better if they have room, lots of room.

Ridgerunner is 100% correct. Multiple roosters can live together and in peace if they have plenty of room to roam and get away from each other, and plenty of hens- at least 8 per rooster. This is only a part of our freerangers below, but the roosters include: Black Copper Marans roosters, 3 PR roosters, a Partridge Cochin, and an OEGB who is flock master. Many of the males are friends, and dustbathe together and sleep next to each other on the roosts at night. They always hang out in groups. The two BCM at right are brothers, and are always within eyesight of each other.