If you're looking for shade, you can have it in a higher ground spot, and put roofing on the roof for shade. If you can't get roofing, a tarp for shade might be good too.
As far as the flooding, I have flooding issues with my run too. What I do is everytime I clean the coop, the shavings go in the run. There's a lot of shavings in the run now, and it seems to be helping. Everytime it rains, the ground absorbs the shavings, so the shavings are becoming part of the ground while help with the flooding. By the looks, I have a much bigger run then your's, so the shavings might work even better for you.
As far as mites, I don't think that water causes those, though I could be wrong. If your birds have mites, they probably got them somewhere else. I don't think the flooding is good because the birds would be standing in water too long, which might cause other issues.
As far as the flooding, I have flooding issues with my run too. What I do is everytime I clean the coop, the shavings go in the run. There's a lot of shavings in the run now, and it seems to be helping. Everytime it rains, the ground absorbs the shavings, so the shavings are becoming part of the ground while help with the flooding. By the looks, I have a much bigger run then your's, so the shavings might work even better for you.
As far as mites, I don't think that water causes those, though I could be wrong. If your birds have mites, they probably got them somewhere else. I don't think the flooding is good because the birds would be standing in water too long, which might cause other issues.