Your external address need to be the address assigned to you(dynamic/static) by your Internet provider. No one can send email to that IP. Or, if the internet connection is through a router or something, the router needs to port forward email to the server and you don't need to be in gateway mode.
For an external Ip(at the time I posted this), I get 212.242.113.186 for hestbaek.net. With that IP I can get your webmail to pop-up and an under construction website. For the email to work, you need to have the default domain or a virtual domain name with hestbaek.net on it.