You'll need to update the link-creating functions, in template-functions.php. Do a search for 'printLink' to find them.
Alternatively, you could add your id to [i]every[/i] link, using the printLink function, but you'll also have to look through your theme for links that use the getXxxx() functions, and add the id manually.
Extra GET parameters (ex: albumname/index.php?id=1) will not affect zenphoto as long as they don't conflict with zenphoto's own (image, album, and page). Use them as you like!