How to show "Caption" in "Advanced Description Field"?

Hi,

Thank you for all the details, it helps us a lot!

1. The image captions are stored as the excerpt, so you can use this configuration for it: https://i.imgur.com/knhDwNP.png
In that case, the {titlefield} pseudo variable will contain the excerpt, which is the caption.

2. That is only possible programmatically via the asp_results filter hook. Based on your description, something like this for a custom code:

add_filter( 'asp_results', 'asp_parent_content_to_attachment', 10, 1 );
function asp_parent_content_to_attachment( $results ) {
	foreach ($results as $k=>&$r) {
		if ( $r->content_type == 'attachment' ) {
			$r->content = get_the_title( wp_get_post_parent_id($r->id) );
		}
	}

	return $results;
}

I have not been able to test this, but it should be close to an actual solution.