Unusual background data usage - which app?

Everyone's billing cycle is different, so being able to have the phone reset each time would be difficult. You can set yourself a recurring reminder to reset you statistics monthly, or at any other interval you wish and you can reset it manually. If you have background turned off, then nothing should be using data when the phone is locked. I suggest you make sure that is off, reset your statistics and keep track of things for a week to see what happens. Otherwise, it is difficult to say what it was.

The battery usage app is tracking usage constantly. The phone does not collect or report your data usage. Why would that be valuable to Apple, since they are not the ones charging you for usage, your carrier is. Your carrier is collecting usage data, it is just that they bill it in blocks instead of each splinter of time that you use data. I suppose if you wish to hound someone about your data usage, you could talk to them, however I'm not so sure they can tell exactly what is doing it, since it is just a data block used by your phone, and the carrier just identifies the device, not the actual data user.

Most carriers are doing their billing at that time, and the phone is not actually using data at that time. I would check with your carrier to be sure. It is probably data from the day before.