Is it possible to let my website show the status message of my facebook page? How can this be done?
There was a discussion about this on the Facebook Developer's forum that might help. The main recommendation is to use the Like Box plugin on your website - although I recommend you have a look at the Profile badges as well.
It's now possible to export your Facebook status as an RSS feed, which means you can add it to your own choice site.
The hard part is finding your personal status "feed." Go to your Facebook Profile page and look for the "Mini-Feed" box. Click on the "See all" link. On the right rail of the resulting page is a list of links; one of them is "Status stories." That's the one you want. Click it.
Now you have a page labeled "My Mini-Feed" that is limited to your own status updates. Look in the right rail for an RSS icon and a label, "Subscribe to these stories." There's your RSS link.
Grab the URL and add it to the Aggregator on your website. Set the refresh time to the lowest possible value (15 minutes) and make sure cron runs at least that frequently.