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Actually I don't worry about their water getting wet when it rains. (Sorry, I couldn't resist) I try to keep it out of the sun in the warmer weather so it stays cooler, but in the winter I use a black rubber bowl and keep it in the sun so it doesn't freeze as much. I think shade on the water in the summer is important.
I agree it is important to keep the feed dry because of the mold. That stuff can kill them. That alone is reason to keep it dry. Another benefit is that it can save money. It is very difficult to come up with a way to feed them that they don't spill some on the ground. If the ground it falls on is wet, it dissolves and becomes a rotten, stinky mess. If the ground is dry and you occasionally let them run out of feed in the feeder (which I purposely do about twice a week) they will clean it up, especially if you feed pellets instead of crumbles.
I just saw the photos. Since you have a net over the top so they cannot get out, you don't have to worry about having something with a roof so steep thay cannot get up there and use it as a launch pad to excape. Somoebody will probably come up with a better way, but I like the idea of a small shelter built against the coop so the coop helps protect it against blowing rain from one direction at least.
We all have different set-ups and conditions. Part of my run is covered, mostly for shade purposes, and part is open. Not all BYC'ers have covered runs. Some don't even have runs but just let their chickens free range. We are all different.
Good luck!