A Smart Calendar and Tasks that can read from mail or give options to add it to Task list or Smart Calendar.
While writing an email, just like smartphones keyboard that knows the user's vocab, hotmail in desktop should know the user's vocab while composing an email. It should smartly assist the user with auto complete and auto compose. This will be an AI feature.
I have always had a tough time search my mailbox. There should be more easy options to search using not just exact keywords but keywords that sound similar, synonyms, etc.
Junk mails should be auto-trashed after a period of days (set by user). This way I don't have to clean the junk mails manually. Even trash (deleted) mails should have an expiry date (user-defined) post which mail gets deleted automatically. Most of my time goes in clearing these 2 folders.
Focused and Others really don't add any value because some of my important mails sit in both folders.
I don't know if this issue is only with Beta, but when I mark my Banking emails as Not Junk, only that mail moves to Inbox. But subsequent mails again go into Junk. This might be a bug but please resolve it. I am sure you don't want us to keep doing folder management every time we open mailbox.
Theme and look - The theme option actually doesn't do any good except changing the top banner background. I was expecting the whole page to change. You need to change the whole page with appropriate colors and also provide option to set the opacity of the reading pane alone. This way the user can define how much of the background should distract the reading.
A chat option for users within hotmail and other linked accounts will make it easy to chat with anyone by logging into hotmail alone.
'Tip of the day' as soon as I open the mailbox for the day with features that can help to be organized will be a great feature.