I can't answer all of your questions, but yes they do fly up onto rooftops, in treetops to roost, etc. My peacock flies up to the top of my house and barn all the time. He loves to go way up high and scream at the top of his lungs. Loud.
They need a lot of space.He roams all over, to visit the neighbors and inspect every inch of my property. My boy was kept in a dog kennel when I got him. It was horrible for him. I kept him confined to a 10'x10' run for months to make sure he knew where home is. He loves to roam and sometimes doesn't come home at night - scares me to death. But he's always back in the morning and keeping watch on my place.
My adults can jump 5 feet straight up without hardly opening their wings. They can fly, but they are not very agile in flight- it is mostly pick a direction and fly in it.
The chicks are pretty big (compared to most chicken chicks) when they hatch, and they only get bigger. They are smaller than goslings.
If by "they" you mean peafowl, they eat gamebird chow, or layer chow mixed with higher protein chow (like kitten chow, or high protein treats like plain greek yogurt or insects). The treats they can be given have a huge range. If by "they" you mean peachicks, they eat medicated game bird starter or medicated chick starter.
I will assume you mean an adult bird. Ideally a trio (1 male 2 females) or quad would be kept in a 10x30 pen. You want, I believe, 80 square feet for the first pea (usually the male) and 50 additional square feet per additional bird. Of course, the more room you can give them the better.
For more info on peas, please visit peafowl 101 and the other lessons available there-after. If you still have questions, come on back and I'm sure we can find you more answers!