Need advice on run materials please

Hi everyone. I'm new here and to the chicken world. I just bought ten acres in southeast Arizona which came with a 10 x 24 chicken coop and a run about twice that size. As nice as that sounds its a miserable, dark, depressing building that has maybe two years of life left in it. I decided to build a smaller coop closer to the house since the current one is completely on the opposite side of the property from the house. The one I built is 8 x 8 and 8' tall. I currently have five hens and what I think is one rooster. They are only about 3 1/2 weeks old. I'm fairly confident in the coop as I put two nice sized windows in and plenty of ventilation. I even insulated it since our temperatures range from 20 to over 100 degrees. What is confusing me is the run. We have about every wild animal here you can think of (bear, mountain lion, bobcat, skunk, tons of coyotes and even more rattlesnakes and gila monsters) And yes, I have seen all of these on the property. So my questions are:
How many chickens can I fit comfortably in the 8 x 8 coop? I have bantams
How big does the run need to be? I will not be able to let them free range much in the summer due to the snakes.
What is the best wire to use? I have plenty of farm fencing (the kind with 2 x 4 openings) and was thinking of using that with 1/4" hardwire mesh around the bottom three feet.
On top I was thinking of using shade cloth so they don't bake in the desert sun.

I appreciate any advice you all have. I need to get the run done pretty soon

You are much braver than I am. With that collection of predators I'd be afraid to step out of the house. You have outlined some good points about your build. I'm not sure how much space bantams require. But for a regular sized chicken space in the coop should be 4-5 sq. feet per bird (not counting roosts or nest boxes). In the outdoor run they should have 10 sq. feet per bird. You coop and run sound plenty large enough for bantams., with room for more.

As for the run, it would be great if you could use 1/2" hardware cloth as an apron around the run perimeter extending maybe 18" out and covered .with boulders or bricks, gravel, etc. That is to discourage digging. I would suggest a strong wire top on the run under the shade cloth. This is to prevent climbers from getting through the cloth into your run - I'm sure bobcats, mountain lions etc. would tear right through it.

I'm not sure if 2x 4 farm fencing is large enough for a bantam to squeeze/fly through and escape. Some banty breeds are very good flyers .The 36" high 1/4" hardware cloth should keep raccoons from snagging body parts and biting them off.

The windows are great, should be backed with hardware cloth, so when opened, nothing can get inside. I've been told many times NOTHING will keep a bear out if he wants in. Including peeling back walls on a steel building. And have no experience with bobcats and mountain lions. I don't know if chain link(like dog kennels) would stand up to them instead of farm fencing. I would still want them backed by the 1/4" hardware cloth.

You will probably get more/better advice posting on your state thread to see how others cope with the heat and predators. I vaguely recall chicken folks using rolls of poultry wire set out in long spirals as a means to keep snakes away. They try to get through the openings and get caught and die there. I've never seen a gila monster and hope I never do.

Are you allowed to use electrified fence wire - I think people run at 3 levels, near the ground about halfway up and near the top. Bears can go through it because their fur insulates them UNLESS they get shocked on the mouth or face. The idea is you set out aluminum foil pieces attached to the wire with a bit of peanut butter smeared on it. When the bear goes to lick it off - he gets a big surprise. He may be shocked enough to pull down the fence in rage but, I've been told he won't come back.

I hope this helps some, I am worried about your predators myself. Hope all goes well for you.

Thanks so much. The predators out here are quite intimidating. Ive fenced and crossfenced all of the property but I'm backed up to a National Park covering thousands of acres where all these critters roam free. I might just get an extra large dog kennel that's chain link and reinforce that with hardwire mesh and the electric fence. Thanks again for all your help.