Custom Page Menus plugin allows custom menus to be defined on a per-page basis.
No, the widget will only output on pages with included Custom Page Menus Widget items. Should a page not have any menu defined the widget will not display anything or affect the layout of the page in any way.
The included pages will be stored in a comma seperated list of ID's in the page custom meta. This meta data might be visible in some WP installs as 'custom field' below the page edit window and should not be edited directly.
Appart from the widget Custom Page Menus can also be included using the template tag: '' This function will accept all the standard wp_list_pages arguments. Note that the featured image can not yet be added via the template tag although this will be added to a future release.