Hello, @Coroveisc,
1- Actually, you have a cache issue because after the update the filter now appears on the shop page before it was not. Check the video for a better reference: https://streamable.com/zizsc9 and check back to your site after clearing the browser cache.
2- No, There is no option in the widget settings to add any class. The thing is when you choose any filter from the site it will appear on the active filter section like this: https://postimg.cc/2VbbMWgG if you remove the active filter widget from the shop sidebar then it will show the checked filter as you said check the image: https://postimg.cc/34t1SGz7
Regards 8Themes Team.