Re: XC5 anomolies - invoice contents, duplicate messages etc.
Yes, this is correct behaviour. If you are using an on-line payment method, you will not receive an initial order notification even if corresponding options are enabled under 'Store Setup -> Contact Information'. That is because online payment method almost instantly can tell whether the payment is accepted or not.
That is why these options only work for offline payment methods like Purchase Order.
X-Cart 5.2 will have a detailed settings page for order notifications though.