Doing big modifications like this should be done with a child theme if you are not already using it so that you can keep Circumference updated.
There’s three parts to creating those icons…the first you already shown the example code.
The second is the CSS which you will find the social icons in the theme’s style.css to see how it’s done for each one around line 649 and begins with:
/* Social icons */
You have three email icons available that you can use. Look at the icomoon folder demo that came with your download to see what they look like and the icon class name such as icon-mail
The last part is the complicated one because it adds the new option setting to the theme customizer. However, I would not recommend you do that because it means you have to create a new function.php file (actually modify one) for a child theme if you want to keep the ability of updating the theme, otherwise you lose everything when you do updates.
I would recommend doing the link manually in the social-bar.php file.