Drupal 7.12 : views filters
Drupal contains a published/unpublished feature by default, which can be filtered in views using the Content: Published filter.

If you want to use a custom field though it should be as simple as you described. Assuming the published field is a taxonomy reference, you should be able to apply a filter to that field and select 'is one of' and the appropriate term (published). I tried this and it works.

As for the second part, you can clone the view and change the field filter to unpublished. Then add a Content: Author relationship and a User: Current (Yes) filter to filter it to content that the current user has authored (you might also want to put some access restrictions on this view). This view can then be added to the 'Footer' section of the first view.