A couple of questions first to understand things a bit more.. then, I'll try to help however I can

* For the SocialShare, it looks like just Facebook is configured.
* You look to have it set to float in the top left of the page.
Are both of those statements correct? Just trying to understand your use case.
As for showing in smaller views, that's something we could look at doing within JFBConnect, but it's also a templating type issue as well. To hide the module in a smaller width layout, it should just take a few lines of CSS media-queries. I'm not sure if that's something we'd add into the module, but it's possible. Either way, let me know the answer to the above, and I should be able to help you with the CSS to at least get you going for now.
Thanks,
Alex