Hi
For Font Awsome. Go to
http://fortawesome.github.io/Font-Awesome/ download the package. Unzip and upload to fonts/font-awesome/, if it's not there create it. Than make sure css file is called. Move css file font-awesome.css from rename it to stylesheet.css, edit this file and change all the paths to "fonts/" instead of "../fonts/"
You can hide or show modules for different devices with mosyledclasses like: "nomobile", "notablet", "nodesktop".
Please attach a screenshot with this white gap. I need to know where to look.