In the Governance Dashboard, you should see the full session logs showing users accessing the published apps.
However, there is no ability in the Governance Dashboard to see what a user has access to. We only report on which apps the user has accessed (as recorded in the session log).
Concerning the distribution task, I cannot say whether you would see the dynamic distribution by doc name.
When you configure the GovDB, do you include the folder(s) where the published qvws live? That would get you the metadata for those qvws.
But with the task, I think it will likely just link to the original qvw and not the distributed versions.