#1. That depends on how many birds you have. The age-old rule of thumb is 1 square foot per bird, but 2 would be better. The more room, the better. But regardless, you must have enough perches for them. At least one per bird so they don't have to fight over them. Also, if you have pairs, then give them a couple nest boxes per pair.
#2. Preferably, yes. Aviaries are good for bathing (both in the sun and the water). I also keep my drinkers in the aviary so the dust and debris doesn't get in the water. If they don't have an aviary, then make sure sunlight is available somehow.
#3. Mine have nested in anything from 14in long, tall, and deep, to nearly 3 feet long, 2 ft high, and about 2ft deep. The bigger ones are my individual breeding cages though, which has 2 nest bowls and a perch. If you can comfortably fit two nest bowls in one box, then that will save you from having to build as many nest boxes. The two bowls will keep them from laying more eggs in the same nest as the babies before they are weaned.
#4. If I remember right, you are somewhere near Salisbury. In that case, you'll be better off feeding them Brown's Pigeon feed mixes. A guy in our club sells a lot of different mixes from that company. He lives in Statesville, but whenever we have a meeting or a race, he brings feed for those who need it, to the clubhouse in Salisbury.
#5. There is no need to trim the tail feathers. Just trim the down feathers around the vent, and you shouldn't have a problem with fertility. The tails are easily moved out of the way during mating. It's that extra "butt fluff" that gets in the way of fertilization. Since fantails are fancy birds, they tend to have a lot of fluff down there.
#6. Pigeons lay 2 eggs per clutch, up to a day difference between them. Once both are laid, both parents will take turns incubating them. The eggs hatch at 18 days, and are then fed by both parents for about 28 days when they are weaned. Sometimes the parents will feed them longer, but you can take them away from their parents at 26+ days. As long as they are eating on their own.
#7. I have a rabbit hutch like that. Put a couple nest bowls in it, and it makes a good breeding cage for a pair. I wouldn't put 3 in there as that will cause fighting over the nest. If you don't let them have anywhere to nest, then it won't be a problem.