Voltage across capacitor - pulse 2a
Suppose, I measure like instantaneously, say after 10us, my capacitor
  fails. Should I not measure after 10us ? If not, why should I not
  measure after 10us ?


Measuring the voltage has nothing to do with failure of the capacitor.


  If I measure the voltage before that 50us, the voltage is going to be
  higher than the capacitor rated voltage. It won't fail? Or is it very
  small time for the capacitor to handle or accumulate?


No one can say for certain whether a given capacitor will fail or not under a brief overvoltage situation. If you exceed the manufacturer's specifications then the probability of failure goes up and, more importantly, you have no recourse with the manufacturer if the capacitor does fail.


  Does the excess voltage go to the load / source? If I have a reverse
  protection diode between the source and the capacitor, then where
  would this 20.937V go when the input voltage has come back to nominal
  14V?


If you connect a load across the capacitor then the voltage across the capacitor and the load will always be exactly the same. If you put a reverse-biased diode between the source and the capacitor then the capacitor would slowly discharge to the source voltage due to the diode leakage current.