Some keep them inside the coop, some outside. Yes, they will go wherever the feed is if they're hungry.
We keep the water inside because sometimes it's 9 am before dh sets them free (usually only on sundays). We keep the food inside because our run isn't totally covered so rain could get in it (from the sides, if we get sideways rain like we did last night).
I keep water inside and outside, but only keep food inside to help prevent the chipmunks, squirrels and other varmints from eating it too.
I prefer outside and then during the winter, move the waterer inside and leave the feeder outside. It depends what type of waterer/feeder you have as well.
I have feeders and waterers on the inside and outside of my coops. Yes, they will go inside to eat and drink.
During the summer, I feed/water mostly outside. During the winter, inside since there may be inclement weather they may not want to battle to get to it.
My small coop has the feeder and water outside, but the feed is inside right now because it's raining. My shed/coop has both feed and water inside. I also have an additional waterbowl outside in the yard. I broke down and bought electric water bowls for winter, best thing i ever did. Thermostat in the plug will turn it on below 40 degrees, off otherwise. You can never have too much water!
Auto-feeder inside with pellets free choice as well as shell and grit, treats outside every evening. LG automatic water inside in their "Florida Room" and homemade automatic waterer outside.