You want to switch from a subdomain (abcd.example.com) to a subfolder (example.com/abcd).
Change config.json to reflect the new url
"url": "http://forum.example.com" -> "url": "http://example.com/forum"
Use nginx to reverse proxy requests by adding a new location block for /forum
Here are steps on customizing Font Awesome. Mayhaps these will help.
Thank you, I'll have a look. Would any updates of the forum affect Font-Awesome in future? Ideally, adding the icon in a way which wouldn't require updating the icons each time would be the best way forward.