WP action/filter to modify title before header output and article output?

The filter wp_title changes only the function wp_title() when it’s called.

So, you must double check on your theme’s source code if before your header is using wp_title.

Anyway, you can set your filter on functions.php. A function to identify your param GET should be something like so:

function maybe_change_wp_title_ver( $title, $sep ) {

    if ( isset( $_GET['title_ver'] ) && 1 === $_GET['title_ver'] ) {
        $title="My New Title";
    }

    return $title;
}

add_filter( 'wp_title', 'maybe_change_wp_title_ver', 99, 2 ); //99 is set as priority (read comments)