CSS are templates, so I'm sort of confused as to what you're referring to. But the CSS is the only way to tackle this. You'll need to use the browser to identify the correct selector to use for your tag and then add the necessary CSS to display the correct icon. (The template would be editor_ui.css IIRC.)
FA doesn't work with sprites because it's using some font icons. The easiest way is use FA is how they were meant to: with extra class:
<i class="fa fa-custom-name"></i>
You can of course recreate all css propertie to an existed html element (you will have first to apply to it the "font-awesome" font-family, etc.) but honestly that's quite a none-sense.
If you want to use FA with a custom BB Code, you can still use the Bbm, there's an option that allows you to select a FA icon (on Redactor or TinyMCE) and applies it to a button: