If they have started moulting, they will llikely slow or stop laying - depending on how hard they pult, the age of the hen, and the hen itself.
Until you can get the door thing straightened out, i do think it is best for food and water to be in the coop - just in case. But, long term, I think it best if they aren't in teh coop. That is just. my opinion, though. I know plenty fo people that have food and water IN the coop, and plenty that don't...

so I guess whatever works for you is what you should do!
The run looks good! They will appreciate a good layer of woodchips - it will attract more bugs and while it will drain, it will also keep the layer of dirt beneath them a bit more moist & give something for worms to work on decomposing - so they will have more bugs and worms to scratch around for!