Can I auto update Civi data w/ data from my listserv?
Assuming you mean a discussion listserv, not an announcement listserv (which would allow you to use CiviMail, or Mailchimp/Constant Contact with the relevant integration extension), you have the option of Mailman integration.  This method of Mailman integration requires that you have shell access on the Mailman server, but it works to sync your users from Civi to Mailman.  So if you wanted someone to unsubscribe, they would use a Civi unsubscribe page, and it would remove them from a group, which would in turn cause them to be unsubscribed from the Mailman group.

Ideally this wouldn't require shell access, but unfortunately, most listserv software simply doesn't have an API.  Mailman 3.0 will have an API, but that's been in development for many years.  I'd considered at one point creating a CiviMailman integration module using PHP-Mailman, but at this rate Mailman 3.0 might be out first!