What a neat start to your "chickening"!!
In response to one of your 1st ?s & statements - if your run/coop combo (coop NOT closed in) is 7x40 that = 280sf. 280sf divided by 10 sq/chicken = 28 chickens in that spot total. That is bare minimum space allowed per chicken. I would not have that many chickens in that area - because during a bad weather spell (hurricane??), they would be completely enclosed there and you may see behavior changes that include feather picking, pecking, chasing and even killing/cannibalizing.
If you make part of the cement area into an enclosed coop - your dimensions change. If you ultimately close off the part by the walk in door for storage, again, your dimensions for the chickens themselves, change. In the coop section, it is recommend (bare minimum) that you have 4sf/bird and the 10sf/bird remains in the run area. Just keep this in mind.
In your area, you need to be concerned more with heat than cold - others have addressed that.
I wish I lived in an area with no predators that would allow me to free range our flock(s) more. I'm a little jealous that they will be able to do that. Might want to keep some sand handy for your walk ways, porch/patio - they will want to perch during the day on the railing. The sand will make it easier to clean up droppings. If your basic area is sand, then you can take sand from that area to use to dust droppings with.
You can do deep litter on the pavement if you have problems with the pine shavings. You can get a truckload of wood mulch. You can use any leaves you get and again yard clippings, garden leavings etc. I have not done a true DLM on pavement, but understand that it can/does work. If you have a compost pile already or a good garden that is not completely planted, take a few shovelfuls of that and add it to the cement area. Don't mix it in yourself or spread it out - in case you do get live worms/bugs (you want those, that's the point), just cover the pile with the shavings or leave it piled up. The birds will then go after the piles and spread/mix it around for you. Hopefully, they don't eat all the worms... LOL. What true DLM is - a living, breathing, biome & bug rich, composting "forest floor". It will "digest" your chickens' leavings, spilled feed and spilled water. It will totally prevent or seriously lower fly population. In a ground situation, it prevents mud, muddy standing puddles and moonscapes. On cement, it makes a forgiving area to land in from roosts and is cooler in summer and warmer in winter than bare concrete (some concrete in Florida summer is cooler, but I don't remember some of the friends' & families being that way - Gainesville - eastern middle/Ft Meyers- coastal). While you will get composting on the cement, you will have to probably pull some of it out sooner than you would from a ground situation as it may not break down as fast. I could be wrong, since I've never done it on cement. As the materials you choose to use do break down, you add more. It will keep going. Again if the the DLM bedding becomes too deep, you remove part of it (not all) by scraping the undigested top back & taking the most broken down part from the bottom and let the chickens spread what is left. Raw materials for DLM are generally laid in so that the spread is 8-12" deep before break down and you add more as it get lower than the 8-12" deep loose/fresh materials. Adding fresh materials gives them something to do, play area, scratching for any bugs that may be in/on the new material. I also add daily veggie/fruit & leftovers from the kitchen/meals and shredded paper/bills (take plastic out) & cardboard.
Since your ground area and coop are now done in deep bedding or DLM, you will want to provide an area for dust bathing when they can't free range and dig in the dirt outside. That is what you want to be a combo of sand, wood ash & dirt. Maybe DE (some say it doesn't work, some say it does - to kill external parasites). I personally would not mix DE directly into any of your coop bedding - especially if using DLM for your garden. I have personally found that it does affect the biome/bugs in my personal gardening attempts (I'm learning in that department myself).
What works in one area of the country, may not work in another.
And like others have stated - "Take a DEEP breath". Slow down, relax and enjoy your chickies. Understand and accept that you will make mistakes - that's how chickening works. Just go on from there. You will find that some things suggested to you will not work - either for you, your situation or your birds. When that happens, change what you are doing and move on. FIND what works for you and your birds.
My chicken journey is very different than many on this forum. While I don't sell birds or eggs or hatching eggs (yet), I have enough birds that many would say we are a farm or a commercial enterprise. I don't really consider myself a "farmer" with only 21 acres (8? maybe cleared), but... ?? who knows. I now have most of our chickens in smaller, tractors - so that they can graze/fertilize the ground but it prevents both the coyote and loose dogs from jumping the fences or aerial predators from dropping down to snag them. Partially a PITA, but it is working for us. We do currently have 7 stationary open air pen/coops (approx 8x8') that get DLM on the stinky NC sand. These coops are w/i reach of areas that we (get real - mostly me) are prepping for gardens - the DLM goes into the beds as we build them - all works in progress, not enough family members right now willing to do the work. Each year, I try some different things. Keep what is working, discard what doesn't.
BREATHE!! and SMILE!! Chicken TV is a great thing (listening to a roo crowing battle right now, myself). Eggs and meat are a good result, too!
