Just tested on your site, and I can't currently use the Login with Facebook button. I get an error message in the popup. That's due to the Facebook Javascript library being loaded 3 additional times in addition to JFBConnect's loading of it. Those extra inclusions will need to be removed. I'm not sure what extension is repeatedly putting the loading of the "all.js#xfbml" file in, but hopefully you can track it down.
As for the share button, one 'hidden' feature in JFBConnect that hasn't been tested thoroughly yet (and why it's not publicized) is a Javascript call to present a popup for the user to post content to their wall. The user does *not* need to be logged into your site or have granted you any permission beforehand. The call is in the /components/com_jfbconnect/includes/jfbconnect.js file and it's functional definition is:
feedPost:function (title, caption, description, url, picture)
So, you *should* be able to create a button that calls the Javascript, like:
<a href="#" onclick="jfbc.social.feedPost('Look at my site', 'Come look at what I found!', 'Great music is here', 'http://www.musicalonstage.be/', 'http://www.musicalonstage.be//link-to-image.jpg');">Click me to share!</a>Again, very untested, but may get you started. You can use an image instead of the "Click me to share!" text, and hopefully will do some/most of what you're looking for.
Finally, for the alignment of icons, I'd start with testing the button above and see if you can get that to work. It uses similar functionality to the sharer.php file, but is supported by Facebook.
Let us know how it goes, and good luck with the options above,
Alex