In Discourse, PMs are topics limited to specific users. So, as discussed above, deletion doesn’t make sense except by staff. If one user were to delete the PM, it would be deleted for everyone in the PM.
What individual users can do is remove themselves from the PM. To do this, select REMOVE under the usernames below the OP, then select the X next to your own username. You will then be prompted with Do you really want to leave this message? - select OK and you will no longer have this PM in your messages.
I agree the UI for this is a bit clunky - maybe we need to make it easier to discover this functionality so people can more quickly opt out of PMs they just never want to see again and practice “inbox zero” also on Discourse.
This is possible. Just flag it for moderator attention, using the “Something else” option. There users can tell the moderators to delete the PM.