Hello,
Take our apologies for the delay in answering.
We have a built-in cache only for the menu and static blocks. So, you need to use any plugin you like to cache all the other things (CSS, JS, page cache etc).
We found that the issue with the All department menu styles appears if you use the File generator. Then additional styles required for this element are overwritten by the core plugin styles. We’ll fix the order of styles in the next theme update. Till that happened just don’t generate the styles file.
Regards