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I have my coop on 24" legs. I wouldn't make the legs any shorter than this, not because of the height of the chicken but because anything lower than this is going to make it hard for you to rake under the coop to clean it out. And there might be a time you'd need to ...ugh...crawl under there to get something out, an egg, perhaps.
Your other question about the headroom is actually pretty important from a design perspective, and that's connected to the ventilation question. You want to have your vents higher than your roosts so you can leave them open or mostly open all winter. So...figure the height of your roost, plus about 16 to 24 inches, then the level of your vent.