Hi,
You can edit these layouts for your back end template via the menu Display->Views. It's the file "form" of the views "user" and "order".
You will have to get the order user id for the order view :
$id = $this->order->order_user_id;
and for the user view:
$id = $this->user->user_id;
before using the $id in some joomla code to get the group of the user.
Here is a thread about that:
forum.joomla.org/viewtopic.php?t=530721
Something like that might do the trick:
jimport( 'joomla.user.helper' );
$groups = JUserHelper::getUserGroups($id);
echo reset($groups);