Hello,

1) The issue with the category icons doesn’t exist on your website. Please clear cache and check back.

Screenshot for Clarification: https://gyazo.com/bbf388b2b971e56d8813e49e3588a4f8

3) Could you please check how it works with some default WordPress themes like TwentyTwenty or WooCommerce Storefront to understand is it our theme issue or not?

Best Regards