Prior to this HW assignment we stored information (such as a list of items) in application scope.  Is there a similar way to do this using databases? or must we retrieve data from the database (and create a list of items) for every servlet that we need data passed to the JSP for?

You must retrieve data from database for every request to ensure that the user always sees the most up-to-date information. In theory you can use caching to avoid hitting the database every time, but implementing caching that supports concurrent updates is rather complex.