How can I add a direct link to the edit account settings page in a menu?
Try this module menu_token , it allows to use tokens in menu


  Menu Token module provides tokens, that could be used in title or in path of menu items (links). For example, if you create a menu item with path: "user/[current-user:uid]", the url will be changed "on fly" to: "user/1" (assuming you are user 1).