I can't receive any e-mails on Office 365 outlook.

Actually it's the other way around. I setup Outlook.com and sent an email from there to my other email account (web based mail.com account). It worked. I then wanted to check if Outlook would get the reply and it failed with the 550 error.

I just tried the same test to a Gmail account on my device and the same problem.

I can go into outlook and send and email, but when I try to reply back it fails.

If you want, give me an email, I'll send you one and you'll probably get the same error.