I just tried the component and the use of Joomla's image function seems to work as expected.
I haven't seen an option for this, so I assume, the fulltext image will be automatically used if set? Or do you just submit the final (onAfterRender) article to Facebook?
It seems that the parameters of the post/content plugins are overlapping with your new Rule Message Control (which is quite a good feature). This is somewhat confusing, maybe you should drop most of the plugin paramters and only use the rule section if possible.
The standard message format seems to be [title] [text]. However, the textfield in the rule is initially empty. Maybe you should fill the field with the standard format to clear things up.
"Media mode: image" still renders an empty H5-tag with some empty space before the link. Not sure if this can be removed.
And finally: Great component. Keep up the good work!