Our developer checked the Business Directory Plugin for a test.
1. Yes, it's compatible, and you can use it with our plugin.
2. I'm sorry, you can't add the reviews on the listings automatically.
At the moment, our plugin shows reviews automatically on WordPress default posts and Wocommerce product pages.
But for the listings, you should add the shortcode of the review manually.
There shouldn't be any problems with the way it works.
Let us know if you need more help, we'll be happy to assist! ;-)