This should include the ability of letting invoice be visible ONLY when the order has been paid or shipped, it has been long talked about in forum spacially from European sellers. Invoice should not be given to the customers until they have paid.
In order notification, invoice should be attached in shipped orders or paid orders, not in open orders. For open or pending orders I suggest just to send a confirmation message with order details or whatever the seller wished to write there.

yes, this is an important feature