Hello and welcome to BYC!
Glad you joined.
Just for your awareness, hens can also grow spurs. Two of my hens have spurs. One has spurs about 1.5" long and the other has spurs about 1" long.
He was not bullying the pullets. He was dominating them and herding them and yes, he looked at you as competition because you were petting and handling his girls. He may become a problem or not. If you just let them be chickens and sit quietly and observe the flock, my boys have no problem with that. Even when a hen jumps up in my lap on her own.
If you are permitted to keep roosters, I would keep him and observe but it is entirely up to you.
Can I also suggest you get some kind of litter in their run? Any dry organic litter for them to scratch through will do like wood chips/mulch, dry pine straw, leaves, etc. And put some perches, stumps, old wood chairs, etc in the run for them to perch on. Try to give them about 15 sq ft per bird at a minimum for space in their confined area.

That is called a spur and they don't develop them to any real extent until after they become roosters at one year of age. Prior to that, he is called a cockerel and and his spur buds will likely not get longer than 1/2". This is also why his crow is croaky. He will also develop a more dignified crow with practice.I was looking for the sharp "extra claw-like appendage" higher up on the leg
Just for your awareness, hens can also grow spurs. Two of my hens have spurs. One has spurs about 1.5" long and the other has spurs about 1" long.
He was not bullying the pullets. He was dominating them and herding them and yes, he looked at you as competition because you were petting and handling his girls. He may become a problem or not. If you just let them be chickens and sit quietly and observe the flock, my boys have no problem with that. Even when a hen jumps up in my lap on her own.
If you are permitted to keep roosters, I would keep him and observe but it is entirely up to you.
Can I also suggest you get some kind of litter in their run? Any dry organic litter for them to scratch through will do like wood chips/mulch, dry pine straw, leaves, etc. And put some perches, stumps, old wood chairs, etc in the run for them to perch on. Try to give them about 15 sq ft per bird at a minimum for space in their confined area.