are you sure the shortcode with the id=’x’ is not working? We’ve tested it again and it’s working on our localhost.
Also, is there a way to call object listings only by type?
You can’t do this with a shortcode, but you can insert the types in your menu. Please go to WordPress admin -> Appearance -> Menu, and choose on the left side in the “Estate Type” box your categories. If the box with the Types is not visible, pleae click the “Screen Options” link to the top right and check all checkboxes.