I want to design a MOSFET amplifier circuit with pulse input. The current and frequency of the pulse is 2.5A and 1kHz respectively. How do I select the input gate capacitor for the MOSFET and what is the purpose of adding capacitor across gate? The input voltage for drain is 5V . How the voltage and frequency of the output is varied if the input capacitor and output capacitor value is varied?
You don't add a capacitor across the input. Any reference to capacitance in the MOSFET data sheet is the effective capacitance that it presents to the driving circuit.
You might want to select a series input resistor for the gate of a few ohms to a few 10s of ohms to control the transient gate input current and the risetime/falltime of the drain current