Okay, first, about your injured quail. Pictures will give us a much better idea of how he got injured and how bad it is.
Second, MyShire is a commercial breeder who stuffs his birds in until they are so crowded that they can't be aggressive with each other because they can barely move. Don't get me wrong, I like Zack. He's a good person and he's always treated people right. If you are a hobbyist and you care about the happiness of your birds, you want to give them a minimum of 1 square foot per bird. The 3 square feet that you have is even better. Make sure they have plenty of hiding places, and you will probably not see much aggression with the three males that you have in there.
With your setup, I would put two separate feeders and two separate waterers in there. That way if you do have some quail that are feuding they won't be able to keep others from getting food and water.
As for your feed, if you can't find a game bird feed, you may want to see if you can find turkey feed. I will disagree with
@Kiki A bit on chicken layer feed. It will keep your birds alive, but if you want best health and best chance of healthy chicks, you want something closer to 20% protein. She is absolutely right about treats, though. Anything that feed that is not a balanced feed is a treat. Black soldier fly larvae are not as fatty as mealworms and they also contain calcium.