Hi!
1. It is not possible. The search can only use the statistics (previous search terms) or the google keywords suggestions database. A similar feature is going to be implemented in the upcoming version.
2. If you have a custom post type called “Properties” then is most likely has custom taxonomy terms as categories. These are not regular categories, they should be listed somewhere under the Frontend Search Settings -> Show the following taxonomy term selectors on the frontend
http://wp-dreams.com/demo/wp-ajax-search-pro3/docs/assets/images/image_36.png
Best,
Ernest Marcinko
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