I don't think it makes any difference if you have a rooster in terms of introducing new birds to your flock.
I can't tell if you've experienced any of the problems you mention, or if you're just reading about other roo's behaviors.
You don't "need" to have a rooster at all, unless you want baby chicks. I would base your decision on that. Or, just keep him, then, if you have behavioral problems, I would sell him or make stew. My free-range roosters never gave me any problems -- there ARE lots of nice ones out there. The only situation I would be take early precautions on, are if you have small children -- because if the roo suddenly showed bad behavior, you don't want him pecking or spurring your kids. If your kids are older than it's not such a big deal to have a rooster fly at them. And if your kids are older, and roos behaves badly, you can get rid of him then.
Typically you should have a ratio of 1:12 or 1:15 hens, but if he's not very aggressive, he may be ok with the 10 hens.
The crowing might be the reason you get rid of him too. If that happens every day, it would certainly become annoying. That's enough reason to sell him -- lack of sleep.