Can I access my Drupal training or development site from off campus?

Under normal circumstances you will not be able to access any site in the drupaldev development area from a remote location.  This is normal.  Drupaldev is intended to be hidden from the "outside" world and Google.

Can I restrict access to certain pieces of content in my site?

Our current system does not allow for true content access restriction at any role.  The only real limit you can put in place is the ability to create or edit specific content types.  Viewing published content is not a granular permission. There are some methods provided here, though, that will allow the ability to, for example, hide menus from a role.  It doesn't restrict the content, it just restricts the path to the content.