Not the OP, but have spent hours on the phone with various levels of Microsoft support...
Basically on multiple browsers (IE 11, Firefox, Chrome) and multiple platforms (Android, IOS iPad) it is completely broken.
I've had a Hotmail account for 20 +/- years so have thousands upon thousands of emails and it would seem like the new web interface is trying to load them all. IOS 9.2 and 9.3x crashes on the iPad when I even try to open Hotmail.com..
This rollout was clearly poorly planned and insufficiently tested.
The only way(s) I have gotten to even partially functions:
-IOS iPhone 9.3... It seems to load only a handful of messages at a time, so is functional.
-Chrome with Scriptblocker on. If I forbid "Onerm-staging-azurewebsites.net" and "swx.cdn.skype.com" it's still a horrifically bad layout, but atleast it's responsive and I'm not looking at 5 - 20 second delays when I try to access or send emails.