I wonder if there's any way to export all orders with status "completed" from yesterday to a excel or csv file (or something similar). This would be done every day.
You can use OrderContext.Search to search for matching orders (SqlMetaWhereClause in OrderSearchParameters can be used). When you have the orders, just write them to excel or csv file as you like.
If you use recent version of Commerce (9.8 or newer), you can serialize them to XML or JSON.