I saw the mention of capons on wikipedia, but I didn't have much information on birds so I just left them off. I still don't know much about how practical or period it is, though it's referred to as an old thing, or how much it extends to the other birds... or alligator pets and so on.
Caponised roosters are definitely documented to before 1600, Your Grace. Apparently it's not a difficult operation, if you know what to look for. I agree that a rooster doesn't have any obvious external genitalia, but I assume that's mostly due to feathers, which hide a multitude of sins. In the modern world, we tend to chemically caponise roosters, which is why blokes who eat enough of the cheaper chicken on the market get a bit much Estrogen. There are farmers out there who do use the old method of caponising a rooster, and having eaten such, I can attest to the bird being larger, fatter, and more tasty than his ballsy brothers. He also grew slightly more slowly. I presume it was due to a low level of testosterone.
chickens reproduce via seminal exchange using a "cloacal kiss". basically, birds have a multi-purpose orifice called a cloaca, through which waste is eliminated, eggs get laid, and sexual intercourse is performed. in many species of waterfowl, an actual penis is hidden inside the cloaca, such as in ducks and geese, but not in chickens, which do not have any penetrating organ hidden inside. instead, seminal fluid is transfered to the female by pressing the rooster's cloaca against the female's cloaca, and squirting it in.
sexing a chicken chick is a very unique skill. there is a slight anatomical difference in the shape of the cloaca, but is not always readily apparent, and can be ambiguous.
yay for growing up on a farm.