No, product integration works only from Prestashop to Holded, therefore any modification made in your products in Holded won’t be automatically reflected in Prestashop.
Yes, stock integration is bidirectional meaning that any changes in the stock will be reflected in both platforms.
Check your Order Status configuration in Holded and see if the assigned numbers correspond to the status of the orders in Prestashop.
Always check the SKU of your products: in order to modify your stock level, the product SKU in Holded and Prestashop 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: