Everything appears on your bill. How it is shown depends on the phone company and if you want fully itemized billing.
The app doesn't need to be open. It registers itself as a NFC handler so when the phone receives NFC comms it starts automatically. Having said that the app typically runs as a lightweight background service so that it can process the transaction instantly (so you can move quickly through the gates at the train station for example), but what I mean is you don't have to do anything to use it, just touch the phone to the payment pad.