What data will be lost when the iPhone battery is drained?

And how long does it take for the battery to be completely drained from the time the phone shuts down?

No.

Nonvolatile memory is used to prevent such disasters.

The battery won't ever be totally drained unless it is left uncharged for a much longer time than anyone is likely to leave it alone.

No data is lost when the battery goes dead. However, once the phone shuts down, you should recharge it promptly, because it continues to discharge very slowly and the battery may be damaged if it discharges too far.