How to adjust the side margins of the side panel to make more room for the logo?

Please go to "Style Customizer > Others > Custom CSS" and use this custom CSS:

#side-container {
    padding-left: 10px;
    padding-right: 10px;
}

P.S. In case you would like to use custom CSS for other elements, I would recommend "Developer Tools" on Chrome or "Firebug" on Firefox to inspect the elements on the page. Then you can know which CSS selector to adjust.