Ooh you got to rehibilate a hawk? COOL!
Hmm, not sure. That'd be for you to decide. If it will protect from a bear, and doesn't have any holes in it, then it should be fine for pigeons.
For grit, I just buy the pigeon grit at the feed store. That should be fine for chickens, too.
You really need to regulate the breeding, as they WILL tire themselves out. For 2-3 years that might work, but you'd need to feed a HIGH protien and high calcium food, otherwise they will lose body condition, become less productive, less fertile, etc. not healthy.
That said, they might not breed a bunch. But once they start breeding, they likely won't stop unless you make them. It's pretty easy - either put fake eggs under them, or boil the eggs and let them sit on them until they're done.
You'll be overrun with squabs in a short time, no issue

if you have 3 pairs, that's 6 squabs a month. If you give each pair a month break after each set of eggs, then that's 4 squabs every month.
Or you can let them only raise 1 squab, then a 2-3 week break. However you should give them at least a solid 3 months break every year. You can regulate it so that its only one pair on a break, and 2 more breeding, so you'll always have squabs on the way.
Personally I like Swiss mondains. But kings are a great breed as well.
Not sure about Birmingham rollers. I like English tumblers. Very cute little birds, I own a cock right now and he's just a tiny thing! Doing great is the cold, too. My swallow pigeon isn't though - had to bring him inside.
A white bird with a crest and muff... Hard to say. Have to have a pic. But, crests and muffs- a muffed pigeon = a pigeon with feathered feet, but in this case I think that birds feet would be called grouse feet. Grouse feet is less feathering, muffed has a lot more feathers - isn't hard to find. Sounds like a roller. Perhaps a Birmingham roller!
You need perches they can lay on. 2x4s screwed in would be sufficient, but pigeons like to lay on their perches, and dowel perches aren't good for they're feet anyways.
And any pigeon can be tame. You either handle them a lot in the nest, or hand raise them. And if your breeding babies, its good to have some Kaytee Exact on hand at all times in case you ever need to hand raise a squab.
Best of luck!
