Let's say a user is visiting my app website for the first time, so I don't know his/her Facebook uid, yet.
Does Facebook provide a widget similar to Like widget that lists Facebook friends of that user using my app (just like it shows his/her friends Liked that page in Like widget in an iframe)?
I remember such a thing however I couldn't find anything similar. Does it exist?
It's called a Facepile. Use it with an app_id, and it'll show the users's connected friends.
Here's the docs: http://developers.facebook.com/docs/reference/plugins/facepile/