In order to add new “X” icon for Twitter in built-in The7 headers, simply download, install and activate this plugin (fig. 1):
Then, add the icon in the usual way through Theme Options -> Topbar & Header -> Microwidgets -> Social icons. You will find it in the end of the list (fig. 2):
For “DT-Contat Info” widget, you also need to select the last icon in the list instead of the old one (fig. 3):
Don’t worry about performance: the plugin enqueues as few resources as any ordinary CSS tweak would do!