Does iPhone Alarm Work When Off ?

When you shut down an iPhone with the power button or using "shut down" from the settings menu, it goes completely off. There are no active apps at all. While some smart phones may go into more of a hibernation mode when turned off, an iPhone or iPad has never worked that way - off is truly off with an iOS device.

It does not work with the phone off. I know this information, due to the fact that it actually happened to me in the past. Hope this helps!

If by "Off" you mean the phone is really powered down and not just asleep or in the lock screen mode, then stedman1 is right - the answer is no. Otherwise the alarm should still work.

No.