I am wondering if there is a way to programmatically read the wall posts of my Facebook Page’s fans (I mean those who “like” my Facebook Page) by either using Graph API or FQL.
I would like to develop an application that aggregates my fans’ wall posts so that I can get to know what kind of people “like” my Facebook Page by reading what they are saying in their walls.
No, you don’t get this level of access just for having had someone like your page. You would need to specifically request access using a Facebook application.