Can I call menu_rebuild() only for one module or specific hook_menu? Is there a way to call menu_rebuild so it will only update items
in selected module and / or hook_menu ?

I need it to update links ( if they are already existing ) and add new
( if they are now ).

Don't want the menu_rebuild to clear the menu_router.
I am afraid that's what the function does. From Drupal docs:


  This function will clear and populate the {menu_router} table, add entries to {menu_links} for new router items, and then remove stale items from {menu_links}. If called from update.php or install.php, it will also schedule a call to itself on the first real page load from menu_execute_active_handler(), because the maintenance page environment is different and leaves stale data in the menu tables.


I guess you could try to reimplement the function into your own custom one and modify its source according to your needs. It looks like a lot of work though. You'd probably have to reimplement more functions.

Source: https://api.drupal.org/api/drupal/includes!menu.inc/function/menu_rebuild/7