No, product integration works only from WooCommerce to Holded, therefore any modification made in your products in Holded won’t be automatically reflected in WooCommerce.
Yes, stock integration is bidirectional meaning that any changes in the stock will be reflected in both platforms.
Check your if your order status in WooCommerce is labelled as Completed.
Why my imported orders do not discount the stock level in Holded?
Always check the SKU of your products: in order to modify your stock level, the product SKU in Holded and WooCommerce has to match.
A quick way to know if a product SKU is related is to create a Holded Document and check if a Box icon appears right next to your item.
To differentiate between each country, do as follow: