Since I have to use Outlook from now on (policy of my employer), I have deleted all my accounts in Mac Mail. Nevertheless, there are a lot of files in the folder "~/Library/Mail Downloads". Why aren't they deleted as well? Can I delete them manually?
This directory is used to temporarily store attachments you open from Mail.app. They should be deleted automatically when you close the attachment. However, if you open an attachment, edit it and save it, then (in my experience at least) the attachment will tend to remain in that folder. Not all apps cause this (e.g. some Apple apps ask you to duplicate the attachment), but some do (MS Office seems to be a culprit for me). You can certainly delete these files manually now, although you might want to check you haven't accidentally saved something important there.