Hello Remi,
A Shopify e-commerce site like any other CMS site can be integrated with the Stuart API, requiring development work which can be simplified using our client libraries. You can visit the post Starting my Integration.
All orders that you automatically create through the API, will automatically appear in the Dashboard. The webhooks are however used to keep track of the status of the orders. Once you create your Stuart account, you can set the webhooks using a specific URL. You can read more information here.
Cheers