The templates query live WooCommerce products by category slug, so any new product you add to the matching category automatically appears on the homepage and category pages.

That usually happens when the theme does not provide the correct WooCommerce archive/single templates or the product category slugs do not match the routing rules. The updated templates fix that.

Yes. Add or edit products in WooCommerce, assign the correct category, and the theme will pull them into the relevant section.