The screen will turn black after a short while once AC Power has been removed.
How long will the battery last?
Roughly 24 Hours, depending on usage and age of the battery.
How do I know when I need a new battery?
While you will get a notification that the batter is low/drained, you will not get a specific notification that the battery is end of life. However, if a battery does not charge when the AC power is connected, and the battery is plugged in, there a good chance its time to replace the battery. Battery replacement is recommended around the 5 year mark.
When the battery dies, I assume we won’t have an alarm system until power is restored, is this correct?
Correct. If AC power fails, and the internal battery dies, the panel will no longer function.