For a Child Theme, do I duplicate the parent style.css and then add my child css?

You’ll never have to copy anything from the parent theme to your child theme. In the case of CSS it would be wasteful, in the case of functions.php it will likely cause errors due to duplicated function names. If your parent theme is badly written it may not enqueue its own stylesheet when it’s not the active theme and you may have to work around that, for example by enqueueing the parent theme’s stylesheet manually in your child theme’s functions.php:

add_action( 'wp_enqueue_scripts', 'wpse425666_enqueue_styles' );

function wpse425666_enqueue_styles() {
    wp_enqueue_style( 
        'your-theme-parent-style', 
        get_parent_theme_file_uri( 'style.css' )
    );
}

Note that this is just an example, we can’t tell you whether this will be necessary because we don’t know what your parent theme is and whether it’s been coded properly to allow for child themes.