How do I update a site after its installation profile is updated?
I don't know if you have any problem using Drush to update the installation profile, but I use git and everything is fine.

If you have code (in the installation profile) that writes on the db and push this to production nothing will happen. So all your changes must done manually.

Finally, the installation profiles aren't the best way to maintain a site, after Drupal install nothing will happen.

About the 40sites take a look at Aegir. It's a hosting platform for Drupals.