Ok, I found a wild pigeon with a broken wing, he/she is now in a cage in my house and is surprisingly tame for a wild bird. But, I have some questions...
Good for you taking the injured pigeon in. I have found ferals are quite tame, even compared to my racers. My racers will fight me when I handle them, and they are incredibly strong, but ferals won't do that. Not sure why.
I am currently feeding it Cockatoo food because it has a massive mix of different seeds that it can pick and choose what it wants to eat. Is this ok? Or should I get a different bird seed mix?
That seed mix is probably fine, just remember pigeons NEED GRIT when they eat seeds. Pigeons like peas (vetch and maple), milo, popcorn, and millet. A mix like that should suffice, so if your cockatoo food has that it should be fine. Pigeons will also do fine with wheat, safflower, and I know some people who keep lofts of ferals that they claim do fine on sunflower seeds alone. Remember, ferals live in the wild and in our cities and seem to survive.
Chicken layer pellets work fine too, and eliminate the need to feed grit, but it will cause their poop to be more runny, and you must make sure the pellet food is NOT medicated.
Shelled, unsalted peanuts make a great treat (pigeons seem to go absolutely NUTS for them, no pun intended), but they are high in fat, so keep them as a treat only and don't over feed.
Pigeons also LOVE greens. Romaine lettuce works, but I have my birds LOVE dandelion leaves. I think they are higher in nutrients. Pick them in the yard, rinse them clean, tie them in a bundle and put them in the cage.
For grit, pigeons should really have a red or gray clay grit made for pigeons, but if you can't find that a chick sized grit mixed with crushed oyster shells should suffice temporarily. If you can't find that type of stuff, try to find a red clay brick and smash it up into pieces no bigger than bird seed and use that. If you soak that in anise or garlic oil the pigeon would be even more inclined to use it.
Perches, it does NOT want to perch and instead just stands on one foot on the floor of the cage, could this be because of the hurt wing or is it typical?
Pigeons typically like to perch higher up on flat surfaces not much smaller than an inch or two, so floor dwelling could be due to the injury or because it is scared or just getting used to being where it is. Pigeons rest with one leg up to maintain body heat I think. The leg thing is totally normal, all my pigeons do it. When the leg is up, the pigeon is resting comfortably, as uncomfortable as it looks to us humans.
I know the water dish needs to be be deep so they can slurp, but does it need to be any other specifications?
I think not, but if it's too deep the pigeon will bathe in it (pigeons love baths) I have found some kind of gravity waterer works best just because they can't soil it. A dish works fine so long as you make sure it stays clean.
As for baths, offer the bird one. They love it. Put a little borax in the water and it serves to kill parasites. If the pigeon drinks the borax water it won't harm the pigeon, but might make its poop a bit runny for a bit.
The bird tried to sleep in the food dish I gave it, and ended up pooping in the food, again, is this typical or something weird?
Pigeons sometimes want to rest in nest bowls. First, don't keep food in with the pigeon at all times. Offer it food morning and night for about 20 mintutes, then remove it. First few times the pigeon may not eat right away, but don't worry, it will figure it out very fast that it must eat when you offer the food. Following the meal, the pigeon should drink then go for grit. Keep a bowl in the cage for the bird to rest in, and a separate bowl for feeding.
Should I give it a nest? If so, what should I do about it pooping in/on it? Also, what should the nest be made of?
Pigeons really don't need nests until and unless they are breeding, so I would say no. Pigeons rest and sleep on perches.
What your pigeon does need, however is sunlight.
If it is female, will it lay eggs in the spring if not exposed to a male?
I think not, but I'm not sure. If you decide to keep the bird, pigeons don't do well alone and you should consider getting it a mate.
Thanks for answering these questions, I'm just trying to keep it from being cat or hawk food since if I can catch it with minimal difficulty outside, I know a cat can catch it.