Adding youtube videos posted to a facebook group to a playlist via script?

I'm interested in finding or developing myself a way to automatically add Youtube videos which are posted to a Facebook group I run to an associated Youtube playlist. Videos are shared by multiple users, not just me so simply using a social networking tool like Hootsuite will not suffice.

I have programming knowledge in web development and object oriented desktop programming, but am not versed in scripting or networking in general.

Do Facebook groups have an RSS or similar XML type feed which I can access given the right authentication? (The group is secret.)

Given such a feed could I distinguish between video posts and non video posts either through some explicit structure of the feed, or by simply searching the data and identifying Youtube URLs via regular expression?

Does Youtube provide an API which supports adding videos to playlists?