#1. the widget “archives products” conflict with our theme:
I checked this widget and it works normally.
Please check Archive template: Archive Product page with “archives products” widget
It’s working now: Product category
Maybe you don’t know how to use this widget and how it works.
#2. Sold out tag:
It’s not the default functionality of woocommerce, so you have to customize it. You can find solution at How to add a Sold Out snippet or badge on a particular product using Woocommerce?
#3. The variation of attributes:
It’s the default display of woocommerce and I see nothing wrong with it