Hi Joergen,
I think the relevant error is
501 5.5.2 <mischianti:>: Helo command rejected: Invalid name
probably you aren’t attached to the Sunrise contract line, and you can use SMTP only with Sunrise line.
For example, if you have a Sunrise cellular line and you try to access SMTP via your home line the provider reject the request.
As test (if you don’t use a mail client) you can try to configure a client like Outlook to send email from the same line.
Tell me if is this the problem.
Bye Renzo