Open eaves are just the start of good ventilation. You will want about half of the front wall of the coop to be ventilation, especially if you are in a place with heat.... and especially if meat chickens will be in that coop.
If the run is at least partly covered then it can shelter the wire...
I would suggest, for over-ground water flow, that you also sculpt the land a bit... and maybe use a run edge that forces the water to each side instead of allowing the water to enter the run.
I have dirt floor coops. They are great, and way better for deep litter. Deep litter is similar to a...