Sending, receiving, and organizing email in Outlook.com
Hello,
The best way to check previous activity on your account is using the Recent Activity page for your account.
What is the Recent activity page? - Microsoft Support
https://account.live.com/Activity
It will show logins and devices used in the past, however it does not go into specifics as to who deleted your outlook emails.
I believe this could be a breach, In my experience when an account is hacked the contents are immediately deleted, rules are set to make the email address a spam sender and then the original user is locked out. Check your email rules and auto-forwarding I also recommend setting two factor authentication to make sure only you who are holding the phone acting as security can access the account. Make sure to log out from all devices as well to play it safe, if there is a breach.
Hope this helps,
JC