I’ve made some changes to your Jetpack settings. Could you give it another try?
If you continue to experience issues, could you let me know what your site URL and WordPress address are, under Settings > General in your dashboard?
Is it possible to republish an old post to Facebook through Publicize, or is it only for a new post?
Publicize can only be triggered for newly published posts.
Why is it when I post an article post URL manually in Facebook, only sometimes does Facebook automatically generate the description and article image, but other times it just pastes the bare URL?
When you share a post on Facebook, or when Jetpack Publicize publishes a post to your Facebook page, Facebook crawls the page and looks for Open Graph meta tags in the head to build a complete post preview (with an image, title, description, …).
Jetpack automatically creates these Open Graph Meta tags for you unless you already use another Open Graph plugin, in which case we let the other plugin handle things.
If some of your post previews don’t look good on Facebook, you’ll want to make sure that your Open Graph Meta Tags are correct for that post. You can do so by checking what Facebook sees for that post, here:
https://developers.facebook.com/tools/debug