There are three cases where email notifications can be sent for any purchase: successful purchases, failed purchases, and refunded purchases. Refunds can only be processed from the payment gateway at this time; there’s no mechanism to refund a purchase from within My Tickets. You’ll need to login to your payment processor to post a refund.
In all cases, an email will be sent both to the administrative recipient and to the purchaser. All messages can be customized, and can be sent either as plain text or as HTML. By default, they’re sent as very simple HTML.
For offline payments, the “Completed” message will actually be sent immediately, without waiting for payment. In the administration, the payment will be marked as “Pending” until you manually mark it as received. At that time, the purchaser will receive a second notification indicating that their payment is completed.
Ticket IDs are not generated until the payment is completed, so for any payment that hasn’t been completed, no tickets will exist.