I really like it and am jealous of your availible space! What are the large back boxes? Nesting or roosting area?
You'll find out what works for you and your chickens as far as space is concerned. The rule of thumb is 10 SQFT per bird of run space. But then you've got huge doors from run to wide open shelter area so your 10X10 run does'nt have to be a lmiting factor. BCY'ers like 4 SQFT per bird for coop space and a bare minimum of 2 SQFT/ large fowl bird is observed. It's all how your set up is, what works for you and your observed happiness of your chickens. I have a tractor (movable coop and run on wheels). The coop space is only 2.25 SQFT/bird and the run less than 4 sqft/bird. But then I let the girls out every day to free range. They only use the coop to roost, are let out of the run the latest at noon every day excepting the rare days we are away. They're happy and it works for me with my alotted area. Chickens hang out together in small areas and it's really that they have choice to "be over there" and then "be over there now" that makes em happy.
So all said and done, yeah, 20 birds for an area that is 10x10 enclosed with a 10x10 run accessed by a huge door would make for happy birds. Putting structure out in your run (like a section of tree with a few large braches to prop it up on side or something) for them to dust bath under or perch on top would keep them occupied too. They do love to climb on top of things and sun bath as much as a dirt bath or just rest in bushes or under my deck...