Answer : A bullet does NOT kill INSTANTLY

As an Engineer, instantly to me is probably 0.02s, the fastest human reflex. But for a physicist, this could be anyway between 0.0002 to 0.000000000000000000000001 etc

Clinically a person is alive as long as the heart is still beating. A headshot would only render you brain dead ... that is said to be INCAPACITATED but still ALIVE (for another 2-4 minutes).