The integration of my private homepage with facebook finally seems to work properly. I had a number of problems, including empty posts to facebook and wrong backlinks to my website but it seems, things are working now.
The reason why I started the integration is that I want to start moving the focus away from facebook to my private website, which gives me more flexibility and control over my content. One important step was the automatic posting of new articles which I write in my private website to facebook.
The next step will be to integrate the facebook login into my website so I can make content available selectively.