House them next to each other for 1-2 weeks, separated by a single layer of wire, then introduce them in an enclosure that is new to all the birds, spacious, has several hiding places and distractions like a dust bath, treats and similar. I've heard it suggested that it's best to introduce new...
I'd separate it no matter who did it, quail tend to be harsh on anyone that is weak or bleeding. 4 males for 6 females is way too much anyway, you only need 1 or max 2 males for 6 females. And one male per cage.
I think the beak might grow back if only a little is missing, but even if it...
You say the ones you checked had a white spot. As far as I know, all eggs have a white spot. If you want to check for fertility, you need to look for the bulls eye - white spot with a white circle around it. If that's not there, maybe your roo is too old? Or maybe the eggs were too old when you...
What are you feeding them? If they don't get direct sunlight where they live, their feed has to contain vitamin D, otherwise the oyster shell won't work. But in general, pelleted feeds have vitamin D and in that case, oyster shell is the way to go. Make sure the pieces aren't too big for them...