Admin only menu/page

Yes, it is possible.

You could use wp_nav_menu_objects or wp_nav_menu_items hooks to add your filter function.

function my_hide_menu_items($objects) {
    if ( is_admin() ) return $objects;

    foreach ( $objects as $k=>$object ) {
        if ( YOUR CONDITION ) {  // if $object shouldn't be displayed
            unset($objects[$k]);
        }
    }
    return $objects;
}
add_filter('wp_nav_menu_objects', 'my_hide_menu_items', 10, 2);

You can also use this plugin: http://wordpress.org/plugins/menu-items-visibility-control/ (I haven’t tested it, so I’m not sure if it really works).