How can I forward a registration form automatically to an e-mail address - as soon as we have a new registration?

Please review the user guide : Explanation-of-Email-Notification-and-Autoresponder-Settings

In the image above, the email address in the Recipient Emails box will be the email address where the registration will be sent.

So in your form,make sure the email address in the Recipient Emails is the one you want the email to be sent.

Hope this help. Let us know if you need further assistance.