Add Links to Pages allows you to add page specific links and have tim displayed through a widget.
Nothing! The widget will not even show up unless the page that is being viewed has links associated with it.
Click the trash can to the left of the links on the add/edit page screen and watch it magically disappear. Make sure you save your page after deleting it though!
Yes! As of version 0.2 you can add links to posts too. Happy days!