What happens if a newly created order is already captured by the Shopify, and the app settings is "Capture and fulfill"? Answer: the app is independent on whether there are capturable transactions or not on an order. If the app setting is "Capture and fulfill", the app will capture if there are capturable transactions.
How does the app work in conjunction with the shop settings regarding automatic fulfilment of orders and gift cards? Answer: the app is independent of the shop fulfilment settings, i.e. gift cards on orders will be fulfilled no matter whether it is caused by the shop setting or the settings in the app.
How does the app handle draft orders? Answer: the app handles gift cards on draft orders as well.