I only keep heritage varieties, which includes palms. Turkeys, especially when younger are prone to shenanigans, and harassing other birds. Once a turkey makes up it's mind about something, like chasing a chicken it will continue to do it for a very long time. Turkeys are much bigger and stronger than chickens so the chicken will always lose out, especially if they can't escape. It will be okay until it's not, than you will have dead chickens.
Some do it, but I would never combine them again, it was a hard learned lesson finding a rooster with his scalp ripped open, and his brain exposed, while 2 toms are repeatedly jumping on him.
Mine now free range in the same area as chickens, but my chickens can escape, and the turkeys get locked back up after a while.
As far as blackhead you won't know it's in your soil until you try turkeys. They will get sick and lethargic, sometimes the head darkens, there will be high mortality rates, I don't know about treatment because I haven't looked into it.