No, but since listings/reviews are custom post types and categories/locations/tags are custom taxonomies, they support WP’s core REST API.
Yes, using the [drts_entity] shortcode. See documentation.
This is not possible but planned for a future version.
Yes. Create a new view, select only “Review Rating” option under “Sort Settings” –> “Sort Options” and use the resulting shortcode on a page to display.
This is planned for 1.2.x.
Not currently. Probable inclusion in 1.2.x.