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?
No - at this point, find my phone doesn't show us any battery status levels along with the location information it provides.
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).