Adding more menu in the menu settings?
Can we add third one here?


Yes, we can. Use hook_form_alter(), alter form_id menu_configure.

How do I know what form_id? Let's see menu_menu() at http://api.drupal.org/api/drupal/modules--menu--menu.module/function/menu_menu/7


  Is there any way to get the list of
  all menus created in backend?


Again, We can. Select menus in table {menu_links} where {menu_links}.menu_name = management.


    $result = db_select('menu_links', 'm')
    ->fields('m')
    ->condition('menu_name', 'management','=')
    ->execute()
    ->fetchAssoc();