Hi,
1. In that case, the simplest would be to edit the order status notification and add the email address you want as administrator to be notified in the "BCC" setting of the email. That way, you would receive an exact copy of the email the customer get to that email address.
The payment notification email you receive as an administrator when the payment notification is received is generated by the payment plugin you're using. It doesn't use the email templating system like the other emails, so you can't modify it to look like the email the user receive. You could theoretically do it (nothing is impossible in programing), but it would be a lot of work for a skilled developer. It will be way more practical to just upgrade to the Business edition and use the BCC feature of the email edition interface.
2. For the other emails that use the templating system, you can edit them via the menu System>Emails (which is the recommended way of doing it in order to not loose your changes when you update HikaShop), but you can also find the files in the folder media/com_hikashop/mail/ via FTP.
3. Leaving blank the "order creation admin notification email address" field will remove the sending of the order admin notifications which are sent to that email address when orders are created (before the payment is made). These emails already contain all the data you would need of the order.