Hierarchical Select Question I don't know if its possible at all but I need something like what is seen in this demo for one of the menus with Hierarchical Select module. This works fine when I use it for a vocabulary with hierarchical terms but don't know how to use it for generic Drupal menus.
You have a separate submodule for using Hierarchical Select with menus, the same as for taxonomy terms.

So, for taxonomy terms you have Hierarchical Select Content Taxonomy submodule (hs_taxonomy), and for menus you have Hierarchical Select Menu (hs_menu) submodule, which you should use in your case.

Click on 'Show config' links on the demo page you have mentioned to see the details.