We don't have any automated way of pushing articles back to Facebook Pages. It's something we're looking into, and hoping to have available in the 4.1 or 4.2 releases.
As for the Google +1 button, my guess is that you have another extension trying to also add the Google +1 button to the page. If so, it may be re-including the Google Javascript library, which has problems when it's on the page twice. Try disabling that and see if it works. If not, let us know your site URL and we'll look to see if there's anything else we see wrong.
Thanks,
Alex
Posting to a page and no +1 button
