Are graded essays written in college marked for destruction considered published work? What is the legal extent the data from essays can be used?
Whether published or unpublished, they are still protected by copyright. (They are probably unpublished for copyright purposes, but in the US this makes little difference for any recently created work (that is anything after 2002). For older work see the Cornell chart.)
They cannot be copied or distributed without permission, unless an exception to copyright, such as fair use or fair dealing applies. And it is hard to see how either would apply to entire essays simply begin placed in a database. Placing text in a database is probably making a copy, and might be distributing it or publishing it, depending on how access to the DB is granted.
Now data from the essays, as opposed to the texts of the essays themselves, are probably facts. Facts are not protected by copyright in any Berne Convention country, including the US, the UK, and the EU.