I'm looking to automate (parts of) the merchant order fulfilment - what's possible?

Most order-specific automation will happen through the status workflow that you define.

Whenever you manage an order and want to change its status, you will need to choose a Status Change, instead of directly assigning a new status. The status change controls the flow the order goes through from the customer going through checkout, all the way through the products getting shipped.

For each Status Change, you can add Status Change Actions that happen when the status is changed. This is where the magic happens. 

By default, you'll find the "Payment Received" status change to be pre-configured to send emails to the customer and merchant, but that's only scratching the surface of what's possible. You could send order and customer information to a CRM or ERP system, have an invoice and packing slip roll out of a physical printer in the warehouse, or do something else entirely. Refer to the extensions list for available integrations.