We have food and water in the run. It only gets put into the coop during extreme weather.
We had one of the bucket feeders, with the pvc elbows...yes, rodents can and did get into it. I stopped using it when I discovered chipmunks in it, during the day. We switched to a
Ratproof Feeder, now the rodents can't get in.
I do remove food at night. Our predators are bear, and I do not want to have things out at night, that attract bears, more than the chickens already do. I usually put the feed back out around 7 am. The auto door has already opened by then, but the chickens are just fine without food, until I get it there. Also, during the fall/winter, I remove water at night, as it will be frozen the next morning, if I don't.