We are working to improve some of the aspects of Facebook sharing; I think you've got some more great ideas in here.
Right now, if you post a link to a Sermons.io sermon on FB, you should get all the proper meta data showing up properly. (Example: https://www.facebook.com/gracechurchaz) However, we just got reports that using the actual share to Facebook button on the sermon page isn't having the results people expect. We're digging into this.
We had auto-posting to FB setup at one point, but had nothing but trouble with the Facebook API flaking out constantly. It may be time to revisit this; you aren't the only one asking for better integration.
I especially like the idea of auto-posting at a certain point in the week. That would serve me too, since I prefer to post to FB on Monday mornings as opposed to Sunday afternoons.
So, it looks like we need to add another look at Social Sharing to our list, in addition to Scripture Browsing, some iOS 9 updates that are coming, theme support that we're working on, as well as a long list of smaller improvements.