Now that Facebook supports XMPP, is it possible to implement a simple bot chat, perhaps through an application (i.e., conversations that are not coming from an individual user).
Maybe late, but yes, you can now write xmpp bot for facebook using any xmpp library. The Jaxl library written in PHP is one of the options for you, it also supports X-FACEBOOK-PLATFORM authentication http://github.com/abhinavsingh/JAXL
Yes! For authentication, you will need a Facebook account. I'm not sure about s2s, but the c2s bot is possible.