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How can I add my own custom icons/fonts to the theme?

Try uploading the files somewhere as a subfolder of the theme and then use @font-face to create a font family.

And then simply add the font-family style for each element you want to have that font.

See here for a description of the process:

http://premium.wpmudev.org/blog/custom-fonts-css/

You can edit style.css or use theme options Styling Options -> Custom CSS