I am currently helping a band set up and customise a WordPress site.
One of the main aims is to establish a central channel to find out about all things band related (live audio/video streams from gigs, gig listings etc) and also post this information automatically to their Facebook Page (not to be confused with a Profile).
My latest trawl of the internet to find a plugin for WP, an application for Facebook or something that works on both sides to feed this info has lead me practically nowhere.
So far I have found WP plugins that allow feeds to personal profiles and FB apps that allow blogs to do all sorts of things with personal profiles but so far haven’t managed to find something that functions using the API customised for Pages…

If you run a business and have managed to “sync” your WordPress site with a Facebook Page please let me know. Otherwise watch this space for development.