$wpdb not being defined in function: Fatal error: Call to a member function query() on a non-object

Okay, new solution. First off, I’d recommend making the link a submit button and making the name something unique:

<submit name 'del_gallery' />

Then in the code of your admin page:

include 'ga-functions.php';
//checks to see if certain button was pressed
if(isset($_REQUEST['del_gallery'] && isset($_GET['gallery_id']) ) {     
    $gallery_id = $_GET['gallery_id'];
    delete_gallery($gallery_id);

    wp_redirect( $_SERVER['HTTP_REFERER'] );
    exit();        
}