Hello,
You can translate/rewrite all theme and plugin texts via PO file in WordPress. Here is a video tutorial that should help you translate your website texts with a Loco Translate plugin https://www.youtube.com/watch?v=D3NsDdMzsls&list=PLMw6W4rAaOgKKv0oexGHzpWBg1imvrval&index=3
Please check the video tutorial to see how to save the translation file correctly. You can remove the plugin and translations would remain. Also, translations would remain after each theme update.
The “Category” sting is one and the same for Shop page categories on mobile.
Best Regards