MOSFET: When can we not assume that the gate current is 0?
Under transient conditions, the gate current will be non-zero since you need to charge (or discharge) the gate capacitance and this requires current.  The larger the gate current, the faster the gate voltage changes and the faster the device switches.  Once the switch transition is completed, then the gate current approaches zero (and is mostly the leakage current).

For low switching (PWM) frequencies, the rms gate current will be low.  Higher switching frequencies will increase the rms current.