We don't have JEvents specific integration, but our social toolbar can be used to publicize any events you've created on your site to your Facebook Page or Group, Twitter Stream or LinkedIn Company page, just like from any other extension or page from your site.
Regarding events in general, you're correct, Facebook recently crippled the API for events. You can edit events that have been created, but you can't create new ones using the API:
developers.facebook.com/docs/graph-api/reference/v2.2/event
I hope that helps, but if you need any more information on the above, please post from the account you subscribed to JFBConnect from. I see you've made a few other posts with questions in them, but it doesn't look like you've ever subscribed. We can't help you further without an active subscription.
Thanks,
Alex