What filter/action hook can I use to add a few links to the admin comments page?

There is no hook. The only place to print something to the screen is at the beginning of the field where $author_url = get_comment_author_url(); is executed.

Sample:

add_action( 'load-edit-comments.php', 'wpse_64737_comment_actions' );

function wpse_64737_comment_actions( $url="" )
{
    if ( 'load-edit-comments.php' === current_filter() )
    {
        add_filter( 'get_comment_author_url', __FUNCTION__ );
        return;
    }

    echo '<p>Output in the Author field!</p>';
    return $url;
}

You can move that output with JavaScript to the bottom of the field later.