Your app works, and works perfectly. The only hiccup I can't quite figure out is how to get it to post to a specific facebook page administrated by me instead of the personal profile.
I put in the page's URL in the setting's under Facebook profile URL, but it posts as my personal account and on my personal account's profile instead. I'm not sure how to change it.
The only other information I can think of that may or may not be relevant is that the page is unpublished until I finish setting it up. I did publish it for a few minutes to see if that changed anything, but I got the same result.