How can I show users the mailings they have been sent?
Yes you can do this with Views.

Important points:


Views must be configured to see the CiviCRM database in settings.php
Create a View for "CiviCRM Activities".  "Bulk Mailing" is an Activity type
The 'link' to view the bulk mailing is probably best constructed via "replacement patterns" within the Drupal View.  You get this link from the mailing itself, before it is sent.  All mailings have a similar link pattern, but each a unique number
Create a Relationship in the view to the Drupal User.  Limit the results to the "current user" or the "logged in user".  I forget the precise wording.  This shows them "their mailings" - rather than everyone's mailings.