My theme saves their custom post type’s metadata as a serialized array, how to access the keys?

That data is serialised PHP, if you pass in a PHP structure it will be serialised into a string. When you pull it back out, it’s de-serialised automatically, e.g.:

$post_id = current post ID.....
$data = get_post_meta( $post_id, '', true );

To see the structure in a human readable form, use something like this:

echo '<pre>'.print_r( $data, true ).'</pre>';

For information about how you would access the information stored in this $data variable, please refer to php.net for basic array and object access [] and ->