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I can't help with the Utah part because i don't live in the US, but i'll try to help with the rest. I've been researching them a lot the last few days, as we're hatching some in August.I don't know the breed of quail you've got, so can't help you there either..
So here's everything I know:
The female to male ratio should be about 3:1, if you get too many males they'll fight and may hurt the females.
For the amount of space, people say one square foot per bird, but seeing as you have an outdoor space and a large chicken run, then I think it would be nice to let them live there. But only put them out once they have their feathers and make sure no predators can get in.
As they're ground nesting birds they won't like to go up to nest, so you can just put a sort of little shed thing in their run for them to hide under.
For the breeding part, If you have the right amount of males to females then they should breed, but keep in mind they're going to be inbred, so you probably shouldn't breed any of their chicks with each other, as after a couple of generations of inbreeding things can start to go wrong. If you work out what kind of quail they are, then maybe in the future you can buy some other quail of the same breed to bring some new blood into your flock.
Other than that I would say, put some things in their run, like rocks, logs, things to climb on and hide under etc.. feed them a food mix with about 25-30% protein once their feathers start growing in, keep their water fresh etc..
I'm still kinda a newbie so here's some other links: https://www.omlet.co.uk/guide/quails/
Edited by Athaid - 5/2/16 at 11:12am
At 1 week old they will still need to be in heat.At week 1 they should be at 95 degrees and drop 5 degreees each week until they are about 5 weeks old.