I don't use outlook hotmail, so can't provide good advice about that service.
There is no privacy in email. The email provider owns the mail and can inspect it, but I doubt it will. Nothing can be more boring than reading people's email.
I guess email copies will remain on web servers for awhile even after deletion, and we can't gain access to those servers to affect erasure. They are not our property.
Eventually they will be overwritten to reclaim space, so you shouldn't worry.
Of course we should be able to erase any copies saved on our computers using Eraser or other document shredding programs.