No rats, just chipmunks (which are rodents at our house). Our run would not be considered secure, as it was made from chain link and not covered in hardware cloth.
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...