It depends on the birds. Ive had boxes on some cages off and on for years and they use them randomly. Some hens will lay in the same spot daily and that might happen to be a box but dont take that a sign theyll all do it.
These are cheap and easy I usually build them for around $60-80 because you'll need to put plywood or 1/2" hardware cloth around the bottom about 2-3 feet high to keep raccoons out.
If you are heating the pen then insulation will function the way you intend it to. For the feeder you might look in the Feeding/watering you flock section of the forum.
Another thing I've found with my auto water buckets, it's best to put a "sight tube" on the outside of the bucket so something reminds you of the water level. When you don't have to water every day, you tend to forget.
I just use nylon bung nipples. I drill a hole top and bottom, the nipple...
If you ever put it in the sun, make sure to insulate the bucket. Even reflective tape all over it is enough, but if you don't the water will get up well past 100* on hot days and the birds won't touch it.