Hi, many thanks for your help.
Grimlock Term Query won’t do the trick. I love the way how it works now, the dynamic filter is just a perfect solution! The user doesn’t need to reload the page. The downside of the current function is the display of all categories, which is impractical for larger sites where posts are used in several completely different places\ways (I have post categories that are not about the news).
If the filters could avoid empty categories (3rd party plugin can show only selected categories, so any other should be empty)that should do.
In this case, I understand only the help of a freelancer is a solution?