Thanks for the reply.
I made a HTML form and a PHP script on a different server, which now is my iframe content on facebook. For requesting the Newsletter membership, the PHP script will send a HTTP request to my WordPress host submitting the email address by a GET variable:
file_get_contents("http://yourwp.com/wp-content/plugins/newsletter/do/subscribe.php?ne=yourem@il.com " );
There is no SSL encrypted connection on my WordPress site, so this proxy works fine for my setup.