Yes, your WooCommerce products will update just like the Factory products.
By default, if you are displaying an affiliate product, there will not be any 'add to cart' buttons.
There are 100s of compatible themes out there. Just pick one that integrates with WooCommerce version 2.1 or greater and you'll be fine. Here are just a few places to find WC themes: https://v4.datafeedr.com/documentation/372
The one you choose is really personal preference.