Hello,
A mosfet is a voltage driven device, the voltage between gate and source determines whether it conducts or not. To compare: a bipolar junction transistor is a current driven device.
There is capacitance inside the mosfet (one between gate and source and a smaller one between drain and gate). To get voltage across gate source, you need to charge that capacitance. The charge required is mostly given in the datasheet. They also mention the capacitances (as function of voltage).
As with a normal capacitor, when you want to charge it rapidly (so high dV/dt), you need to apply a large current pulse for a short time. It is not strange to apply Amps during some ns.
When you want to make the voltage zero (mosfet off), you need to remove the charge (that is charge from Cgs and charge from Cgd).
The so-called gate leakage current is generally very low, typically nA range.