Adding deliveries does indeed have to be done through the backoffice web pages rather than the EPOS app, but of course you can easily log in to the backoffice with a browser on the same tablet you use for the app. And if you use a barcode scanner you can enter your deliveries by scanning barcodes rather than having to search by name.
I am a programmer by trade (it’s mainly my wife who actually runs the shop) so I’ve written my own small bits of software to automate the pulling of sales from AirPOS into QuickFile, but it should be straightforward to do by hand with the QuickFile cash register tool - each Z read in AirPOS becomes one row in the tool and you just have to enter the cash total, card total and VAT (if you’re VAT registered).
If you’ve been using a retail VAT scheme you won’t need that any more as AirPOS calculates the VAT to the line level on every transaction.