Should I use a gate resistor for FQP30N06L if my gate is connected to GPIO 3.3 volt of a Raspberry Pi?
I put a resistor between GPIO and gate, then the resistor is going to
create a damping effect. Right?

Yes. Series resistance is good. Without damping the Gate capacitance and wiring inductance form a high Q tuned circuit that 'rings', causing possibly unacceptable EMI or even circuit misoperation.

The higher frequency I have, the less voltage is going to attach to
the gate pin of the FQP30N06L?

Not exactly. The resistance and capacitance form an RC low pass filter. With a step input this causes the voltage to rise and fall according to the equation \${Vc}(\text{t})= \text{V}(1-\text{e}^{\text{t}/\text{RC}})\$, like this:-

The result is that the FET turns on and off slower, spending more time in the 'linear' region where it has both significant voltage across its Drain-Source channel and current through it. Power = voltage x current, so it will heat up more than with fast transition times. How much more depends on the transition time, supply voltage, Drain current, and PWM frequency.

The threshold voltage is between 1.0 to 2.5V for the FQP30N06L.

At its threshold voltage your FET is just starting to turn on, limiting load current to 0.25mA. To fully turn on it needs 5V or more. At 3.3V you will be lucky to get 1 A with a voltage drop of 1 V, dissipating ~1 watt of power in the FET. If you are unlucky and your FET has higher than typical threshold voltage it will be even worse.
Worse again, the RC charging waveform slows down as it approaches 3.3 V, so the FET will turn on much slower than it would with higher voltage Gate drive.
As these graphs from the datasheet show, 3.3 V Gate voltage typically limits current to between 1 and 2 amps, and doesn't even reach the plateau voltage (horizontal part in figure 6) where the FET turns fully on.


To fix this you could use a simple level shifter like this (which is readily available as a module for I2C applications):-



simulate this circuit &ndash; Schematic created using CircuitLab
Alternatively you could just use a FET rated for 2.5 V Gate drive.

the GPIO is going to PWM about 100-300 Hz.

This is good. The low PWM frequency means the FET only transitions through the linear (high power) region a few hundred times per second, so slow turn on/off times will probably be acceptable if the Gate voltage issue is addressed.