1) What is the definition of input capacitance of a pin in an IC?
It's the capacitance from that pin to ground or 0 volts.
2) How is it measured in the first place and is it applicable to all Pins in the IC?
It's probably not measured on production items; rather it is essentially always that value unless there is a significant production anomaly on the die. It's applicable to signal inputs.
3) And Why should we care about this parameter of the IC while we design our circuit and how is relevant?
It's a very relevant parameter given that a signal with significant source resistance will have difficulty keeping its rise and fall times short/fast with too much input capacitance.