Outlook.com does not accept most mail.

I was recently converted from Hotmail to Outlook.com. Here are my issues with outlook:

1. I receive only emails from the Outlook Team.
2. I can send emails successfully.
3. As a test, when I reply to the email (item 2) from my other account the reply is received by the alias account and not Outlook.
4. Emails to my Hotmail address are received only by my old Hotmail account.

Your help is appreciated.