Hello Bill, and welcome to BYC!

Glad you joined.
You truly do NOT have extreme cold there. You may have some cold spells. You need to focus on keeping chickens cool. Breeds with large single combs can keep cool easier.
It all depends on the dogs prey drive and trainability. Its very dependent on the individual dog. I keep my flock behind electrified poultry netting so my dogs steer clear.
A rooster will stay on alert as well as guinea fowl and would likely be less noisy. The flock should be secured in a predator proof coop at night so that should keep them safe from owls. Offering overhead cover from hawks or keeping them in a run with a roof on it is the only way to completely protect from aerial predation.
You can modify a shed into a coop. In your area, I would have large roof overhangs and remove entire walls and cover them with 1/2" hardware cloth over the studs. The studs would need some kind of weather proofing. Or remove the top half of the walls and cover with 1/2" HC. You can cover some/most of the open areas with tarps to winterize.
You should offer 1 linear foot of roost per bird and the roosts should be anywhere from 1 to 4' off the floor. You need one nest box per 4-5 hens. You need 4 sq ft of floor area per bird. Nest boxes need to be positioned lower than the roosts.
Not necessary. I prefer the use of poop boards that get scooped daily. I clean the coop floor bedding out annually.
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From the moment they push the shell off themselves. You can brood directly in the coop with a mama heating pad or brooder plate.
Mediterranean breeds. Flighty.
They can't. They can only run to cover.
He can alert the hens to predators giving them a chance to get to cover. They can and will attempt to protect their hens by fighting a predator but will lose. They were designed to fight off rival roosters, not coyotes.