Emails are not sent to outside domains
I solved the problem.

Taking inspiration from this thread, I figured out that, for some obscure reason, I need to set the email setting under "Administration > Configuration > System > Basic site settings > E-mail address" to an existing email address on my hosting service.

So, I created a new email with cPanel, noreply@mydomain.com, then I setted this email address in the above configuration.

Now seems that all is working perfectly.