Will I be able to use Find iPhone if my battery is dead? Will the location of my iPhone be updated if the battery is dead? Is there any way to know if the battery on my iPhone has died?
On iOS 7 and a newer version of Find My Phone/iCloud, the battery level is reported so you can know approximately how much longer the tracking might be active without a recharge.

When this question was asked, the battery level was not shown so the answer then was no.

Either way, once your iPhone runs out of power, it will shut itself off. There is residual power left in the phone to run the screen and respond to buttons for a while, but once that last remaining power drains, eventually the voltage in the battery is not sufficient to run even the button sensing part of the device.

Plugging it into power will re-start your phone and once it establishes a network connection, find my phone will resume.

In your case - if Find My Phone says your device is not found - you can't really tell if it was turned off by intention or automatically or has lost network connectivity (by having a SIM removed or just being out of range).