Sadly no, this has to be done entirely by yourself.
In Runescape bird eggs can hatch into either Saradomin owl, Zamorak hawk, or Guthix Bird depending on the color. To get them to hatch you need 70 Summoning. Yo can get a bird egg by randomly getting one in a Birds nest from a tree. Links below
Anything from 1 - 3 days, depending on the bird.
You have to have the proper Summoning level along with a Baby Bird of some kind. The you would ask one of the many Pet Shoppe owners around Runescape about what to feed it.
You can tell what bird it is by colour.
Yes it does, an Eagle is a bird, all birds hatch from an egg.
Birds lay eggs.
Yes it does, an Eagle is a bird, all birds hatch from an egg.
A peregrine falcon is a bird of prey, and the chicks do hatch from eggs.
nuthatch
there is no such bird.
You will need a Bird Trap these can be bought at Yanille hunter shop.
For a bird to hatch, it takes about 2-3 months. My class did birth of chickens and it takes 2-3 months.