[Kalais]

Would this be possible:

Add an option to the context menu that when I highlight over a specific clickable link (within a non-library addon), it would copy that link address to be added to a specified menu shortcut? Eg. Highlight "Search," open context menu, select Add to Menu, then a dialog box opens allowing you to select or create a new menu shortcut

This is already possible - have a look at the Context Menu add-on 'Skin Shortcuts - Add to menu'

Worked just as how I asked however it pops up with a Skin Shortcut error everytime I try it.