At that age in that situation his behavior sounds pretty typical. I raise several cockerels and pullets with the flock, usually 4 or 5 broods per year. Some are brooder-raised and some broody-raised. Typically when my cockerels reach puberty they bother the pullets their age first and the dominant rooster ignores that. But eventually one starts bothering his hens, he does not like that. If the dominant rooster is in the area he'll chase the boy away. If a hen is out by herself and a cockerel starts bothering her she runs to the dominant rooster who handles the situation. He usually does not chase the cockerel down and beat him up, he just runs him off. One year I did have a dominant rooster that did a lot of chasing but that cockerel needed a good spanking anyway. Each year is different in some aspects.
I usually eat the boys (or the dominant rooster) before a cockerel is old enough to really challenge him. At some point Junior will probably mature enough to challenge the dominant rooster but until then expect to see more chasing and running away. Sometimes they fight to the death when they do fight or one might get seriously injured. Often they reach an accommodation on how to take care of the flock together. The more room you have the better your odds of it working out. But I suggest you have a plan so you can immediately separate one of the two boys if you need to. Even if you have an all-hen flock I think you need something like that.
Occasionally a cockerel (or pullet, or another hen) threatens a broody's babies. Immature cockerels are probably the worst. My broody hens have never failed to protect their babies. I won't say the broody hen whips butt, she often doesn't get the chance. A mad broody hen is so scary the others run away before she has a chance, even if they are bigger. It usually doesn't take long before they learn to leave her babies alone. Not long at all. Some people say their broody hens don't protect their babies. I certainly believe that can happen but I haven't seen it.
I have no idea how your situation will work out in any aspect. With living animals I can't give guarantees with respect to behaviors. What you describe is very familiar, it happens every year with my flock. My suggestion is to observe and base your actions on what you see.
If you want to keep him, consider building a separate coop and run for him and keep him isolated if you need to. Many breeders do that type of thing if the boys can't stay together in the main flock outside of breeding season. If you are going to breed him to certain hens you'll need a breeding pen anyway.
Good luck and let us know how it goes.
I usually eat the boys (or the dominant rooster) before a cockerel is old enough to really challenge him. At some point Junior will probably mature enough to challenge the dominant rooster but until then expect to see more chasing and running away. Sometimes they fight to the death when they do fight or one might get seriously injured. Often they reach an accommodation on how to take care of the flock together. The more room you have the better your odds of it working out. But I suggest you have a plan so you can immediately separate one of the two boys if you need to. Even if you have an all-hen flock I think you need something like that.
Occasionally a cockerel (or pullet, or another hen) threatens a broody's babies. Immature cockerels are probably the worst. My broody hens have never failed to protect their babies. I won't say the broody hen whips butt, she often doesn't get the chance. A mad broody hen is so scary the others run away before she has a chance, even if they are bigger. It usually doesn't take long before they learn to leave her babies alone. Not long at all. Some people say their broody hens don't protect their babies. I certainly believe that can happen but I haven't seen it.
I have no idea how your situation will work out in any aspect. With living animals I can't give guarantees with respect to behaviors. What you describe is very familiar, it happens every year with my flock. My suggestion is to observe and base your actions on what you see.
If you want to keep him, consider building a separate coop and run for him and keep him isolated if you need to. Many breeders do that type of thing if the boys can't stay together in the main flock outside of breeding season. If you are going to breed him to certain hens you'll need a breeding pen anyway.
Good luck and let us know how it goes.
My rooster will run and chase him away occasionally, but no fighting so far (I know it's coming). The young boy also gets upset when my rooster mates the hens. The other morning I saw my rooster mating a hen, and the cockerel was on top of the rooster while this was happening. 
