Facebook has its own pool of developers to create apps for the site but if you are interested I think this page on softwaredeveloper.com gives some great tips and links. Hope that helps. Have a good day!
Yes but it takes time, and a lot of trial and error. but if done right you can make quite a bit off facebook.
Income from Facebook? In what since you are asking this question. If you are talking about product promotion then you can earn form Facebook.
Well, you may look for business who want to promote their website or want to market their Brand in Facebook.This way you can make some money through Facebook