Chickens don't need a rooster for anything. His biggest job is to strut around and make noise while they're in the nesting box. ostensibly "protecting" them while they are vulnerable. The theory is that hens are "happier" if they feel they have the protection of the rooster. Hens lay the same with or without a rooster.
An 8x8 enclosure would be fine for as many as 8 hens. When the dogs are inside you could even let them free range some. They'll go back into the enclosure to roost as soon as it begins to get dark and you can close the gate.
I've never had an issue with chickens being particularly nasty. Once in a while I put a bail of woodchips down or a few flakes of hay. When I rake leaves a wheelbarrow or two of leaves go in there and every now and again I rake it all out and dump it in the garden.
Mine roost on a wire shelf so the poop doesn't accumulate on the roost. Bugs live under the bedding on the ground and the chickens scratch in it and eat the bugs. Laying hens need a feeder with "Layena" feed which is fortified with lots of calcium to make eggshells, and a daily ration of scratch feed(mostly cracked corn and millet) thrown on the ground. And, if you want better eggs than the grocery store variety, they need some green stuff.
I've had chickens in Florida for around ten years and have never had a problem with mites, in your arid California climate I don't think you have them at all. I understand they are a big issue in the UK.
Once you get set up chickens require practically no maintenance. Check the feeder, toss in some scratch feed, gather the eggs and you're done for the day.
