It would be nice to have some photos of the rooster, his poop and the inside of his beak.
How old is he?
Check to make sure his crop is emptying overnight. To do this, feel of his crop when he goes to roost, you should be able to feel a bump or bulge on the right side of his breast, this is the crop (food pouch). Next morning, go out and feel the same place again before he's had anything to eat/drink, the crop should be empty/flat.
If he roosts high, then caging him for the night be easier to gauge crop function and get a good look (and photos ) of his overnight droppings.
Do look inside his beak for lesions, canker or yellow pasty material.
How long have you had him?
If the windows stay open in your coop, then like ventilation is fine. The building is not airtight.