Say if I already know the Facebook user's unique ID and got the user's extended permission, is there anyway that I can get to know whether the user has Liked a specific Fan Page?
The Like Page is not my Facebook App Page but OTHER 3rd party's Pages. E.g. Volvo Fan Page, Nike Fan Page, etc.
Can the above be done?
Yes. You can use-
/<user_id>/likes
to get all the pages this user has liked.
Permission required: user_likes