Expand region to fill screen size
You could style that special page with css to not display the footer (display:none). Drupal delivers a css class in the body tag that identifies the current node, like so .page-node-x, where x is the node id of the page. So you could go like page-node-x .footer.

You could also use a page.tpl override for the specific page where you remove the footer region. Create a copy of page.tpl.php in your themes template folder and name it page--node--x.tpl.php. Remove footer in this file completely.

And as for fullsize background image, maybe this module could be interesting: https://www.drupal.org/project/supersized