Hasan,
1) What's happening when you try to use the SCLogin module in Chrome or Firefox? In both browsers, I'm able to see the button. In Chrome, I clicked on it and was properly brought to the "Login / Register" page of JFBConnect where I could have created an account.
Please let me know what you are, or aren't seeing happen with as much detail as you can provide.
2) Unfortunately, JFBConnect will not do what you're looking for. It may be possible to do all of that using the Facebook API, which JFBConnect implements and tries to simplify, but you'd definitely need a developer to create the connections you're looking for. If you have a developer, we can gladly provide a few pages of documentation on Facebook that would be a good starting point as well as some tips, but it's not something we'd be able to develop for you.
Hope that helps,
Alex