In the old Outlook.com you would configure your business email address like myname @ mydomain.com to forward emails to your Outlook.com account and as a "send only" account so you could send emails from that address.
After the forced migration to the new Outlook.com this feature has been removed. The only way to send emails on your business email address is to set up a POP account (IMAP does not work reliably at this time).
However Outlook.com only collects mail every 30 mins so that is very bad.
What is the best configuration?
(see my reply for the answer)