Hi,
To change the order, you can edit the mail in HikaShop > System > Email, and the invoice in the view "order / invoice" in HikaShop > Display > Views.
Then in the edition page, you can change the order of the elements. Move elements between <tr></tr> tags up or down another element.
Example of an element:
<tr>
<td colspan="2">
</td>
<td class="key">
<label>
<?php echo JText::_( 'HIKASHOP_PAYMENT' ); ?>
</label>
</td>
<td>
<?php echo $this->currencyHelper->format($this->order->order_payment_price,$this->order->order_currency_id); ?>
</td>
</tr>