I don't know for sure about anything in the Repository (althought maybe working with document locking might be an option - maybe there's a way to track and report on when and how long a document was locked).

As far as Forms is concerned, there are some things you could try.  Of course you can use the built-in functionality to auto-populate the date and time of fields just using the default values, but that will only track when it was submitted.  If you wanted to track when it was opened, you would need to leverage Javascript.  You could have Javascript that stores one date field when opened and a second when submitted, and then use Workflow to move those values into a database or wherever you wanted it tracked.  This of course assumes the form is actually submitted, you wouldn't be able to track a form that gets closed without submission, since by definition Forms only saves data upon submission.  I'm not certain you could get anything better than that without an API or similar external functionality.