He did say gate-source.
In the datasheet, such a diode - two back-to-back Zeners - is shown.
What board is that?What board is this? Where is/ was the link to a board?The gate grounding resistor is to keep the FET switched off when the Arduino is reset and its pins are effectively inputs and may float. Since this problem belongs to the Arduino rather than the FET, the resistor should be across the Arduino pin to ground. If it is on the FET gate, after the series resistor, then it tends to form a voltage divider and reduce the voltage turning on the gate. That may be a minor effect, but it makes sense to avoid even minor impediments to performance.To protect against ESD (Electrostatic discharge).