Hi,
Well, it is sort-of hard to tell without actually seeing the configuration, but my guess would be, that there are either categories excluded, or the taxonomy logic might not fit your needs. For that, I would first suggest changing this option as follows: https://i.imgur.com/Xogs4IG.png
The further filtering on the results page is possible, if you place the same search instance as a widget/shortcode onto the results page. You can also try the live results loader feature. It may not work in some cases, as it highly depends on the theme implementation.