Even when injured or ill, the birds are fairly low-maintenance. They don't require constant care, but rather only periodically throughout the day. As long as the bird has a safe place to rest, and is eating, drinking, and passing droppings that show that food is making it through the bird's system, they can recover from pretty-much anything -- horrific wounds, debilitating disease, etc.
I bathe birds in a large mixing bowl about 1/2 filled with room-temperature water. Add 1 teaspoon of boric acid per quart of water to kill and/or repel mites. Feral / wild pigeons generally have mites and/or lice, and pigeon flies, none of which survive for long if they aren't on a bird. Since your bird has some paralysis, don't leave him in water, and when he is able to drink by himself, don't give him a water dish that is large enough for his head to fall into to the extent that his nostrils would be underwater. Use something shallow and heavy like a small, clean, glass ashtray. Pigeons and doves use their beaks like a drinking straw and can sip water even if it is only as deep as a dime is thick.
Add a little bit of lemon juice to his drinking water for electrolytes, and the birds actually seem to like the flavor. About 1/4 teaspoon per cup of water. My
formerly feral pigeon friend here is healthy and drinks a couple of sips of water in the mornings after eating seeds. She drinks a couple of times during mid day, more if the weather is hot. Mid day is when she seems to drink the most volume of water too - three sips each time instead of the two sips in morning and evening. Then in the evening she eats and has two sips again before sleep. Since your bird may be sick, he might want more frequent water, and possibly more volume of water too, but I wouldn't force him to drink if he is able to do so by himself when you hold the water up to his beak.
It would be good to look inside his beak and throat for any orange or white colored spots. Normally the tissues are all a similar shade of pink or red. If there are orange growths in his throat / esophagus, they may grow so large that food can't pass to the bird's crop, and in which case he'd need a diet that is more liquid, mixed with a powdered formula. If there is nothing blocking his esophagus, then he can eat seeds.
He is probably vitamin A deficient, most feral pigeons are -- so a few tiny bits of carrot or bell pepper each day may make a big difference in his recovery. Raw, unshelled sunflower seeds, dried peas or split peas, barley, lentils, rice and other similar seeds and grains are all good food for the bird. Don't feed him dry, uncooked beans though as they have lectins such as hemagglutinin that can cause digestion problems, diarrhea, and death. There are a lot of naturally antibacterial and antiviral foods (see the Natural Remedies link in the signature at the bottom of my posts) that are both nutritious and helpful in fighting infections. Some like raw Apple Cider Vinegar are added to drinking water. Others can be fed to the birds just like seeds -- if he can't eat on his own, slightly squeeze your fingertips against the sides at the base of the beak to get him to open his beak, place a seed or bit of food inside and then let him swallow.
Normally, adult pigeons eat from 1.5 to 2 ounces of food per day, which is about 3 to 4 level tablespoons of seeds although it varies by the density of each type of seed. The adult pigeon here, whom I call Sky, likes to eat some seeds about a half-hour after waking-up (we both get-up at dawn), and a couple of times during mid day, then once in the evening prior to going to sleep.
Line his box or sleeping area with paper towels for easy clean-up of droppings. Also, if you post a picture of his droppings it may help to determine whether he has an illness vs. physical damage.
Oh, and calcium deficieny is common in indoor birds but not in feral pigeons. They have all the sunshine and limestone they need usually, so he probably isn't calcium deficient at this point, though adding some vitamin D3 to his diet (hard-boiled chicken's egg yolk is a good source) while he is recovering would be good since they can only get it naturally through exposure to direct sunlight. Some seeds contain enough calcium by themselves (sesame seeds, flax seed, raw and unshelled sunflower seeds, oats, and rice as examples), and offering "pigeon grit" (any of crushed limestone, oyster shell, or boiled chicken's egg shells) is a good supplement.
