If my product sells on one site, will it automatically on other sites it is listed on?

As long as you're using the save Vendevor account to manage all of your products - Yes!  Vendevor manages your product inventory for you, so if an item sells in one location then all of your other sites are updated.

For example, if an item shows as 'Sold Out' on your website, the store connected to your Facebook page contain the same information.