Hi,
The first one is in the email that you receive as an administrator. That's why the link points to the backend, because no one else besides the customer is allowed to access an order from the frontend, and as an administrator, you have access to the backend, and it will be more interesting for you to access the order from the backend.
For the second one, you can modify it to look like the third one. It requires editing the order status notification email and add such line at the beginning:
Code:
<?php $data->order_url = hikashop_frontendLink('index.php?option=com_hikashop&ctrl=order&task=show&cid='.$element->order_id.'&Itemid=XXX'); ?>
where XXX is the id of your "account" menu item that you can find in the Joomla menu manager.
