Uhm, what you set on main newsletter config for sender, return path and reply to? Try to empty the latter two and set the sender as you see it to come from contact form 7. Have you setup an SMTP on Newsletter configuration OR have you an SMTP plugin that make WordPress to use an SMTP to send emails?
For sure it can be a big problem to use an email on a different domain than the one of the blog. You web provider could drop the outgoing messages. More, the sender email should be a real existing email.