Welcome, it's so nice to see such a wonderful offer.
I'm sure you are reading a bunch on here about how to take care of the pigeons, and we would be happy to answer any questions for you.
You asked about the males; generally males get along just fine as long as there is an equal male to female ratio. Pigeons mate for life (or until separated by someone or something) so once they chose a mate, they are content to have a nest box and a roomy flight pen to hang out in. You can use fake eggs so that they don't keep reproducing, as they will lay all year if the weather is not freezing (and sometimes even then!)
Any adopted birds would likely need to be kept "prisoners", which means they can't fly free. Most of the birds for adoption, like Reti's, are used to being in cages or enclosed areas so this is not a change for them. I have had "prisoner" birds, mostly rescues, for nine years and never had an issue with one trying to get out. They are, with rare exception, content to have some room to fly, a mate, food and water, and a warm, dry nest box.
Are you planning on setting them up in a pen outside? If so, you could build a small aviary/flight cage for them pretty easily. Depending on how many you have, you could start out fairly small and always add on later if you decide to have more. It's best to use 1/4 hardware cloth for the wire as it's the safest against predators. Some simple wooden square nest boxes work well, or even old bookcases, old furniture, or similar things. It's easy to improvise if you're short of funds, trust me, I know.
You can find a pigeon seed mix at your feed store, sometimes they have a few. It's much cheaper usually to buy it by the 50lb bag, around $20. They should have red grit too, which pigeons need to digest their seeds. Store it in a sealed container, because if it gets damp at all it can mold and be toxic.
They enjoy a bath dish (plastic cat litter boxes work well) pretty much whenever you feel like giving them one. The little chicken waterers work well for just a few pigeons for drinking water, and you probably have one or two of those laying around already.
Which reminds me to mention we've found it's best not to let pigeons and chickens mingle or live together, as even the nicest chickens can kick a pigeon's tail.
All in all, it's pretty easy to keep pigeons. Just a water change and fresh food and grit everyday, and a scraping inside the aviary when it needs it. They're just as fun to watch as chickens (I love chickens too) and each one has such an individual personality, they are wonderful and smart birds. I hope it works out for you adopting some from Reti and the NY one, and like I said please ask any questions you think of.
Good luck with those roosters, too.