Hi,
When I switch back to a 'created' state and then back to 'confirmed' with 'inform client' I get the confirmation message but no invoice either.
If you turn on the "user notification" option in the popup, you will get the email.
Regarding the email which has to be sent when the orders are confirmed automatically, That is sent normally by HikaShop if the payment plugin sets the parameter:
$order->history->history_notified = 1;
before saving the $order object (with the new status).
If you receive the other emails, I doubt that it comes from the setup of the email settings and I would say that this payment plugin does not activate the notification. In that case, you might want to ask ccIdeal's support about that.
Otherwise, if you don't receive the other email (when changing the status with the notification option activated), then it's either a problem with the email itself or with the email settings. In that case, did you change something in the email ?