If you're switching an inductive load the diode typically goes across the load. This is because a reverse voltage is generated when power is removed. The diode serves to redirect it away from the transistor (which it would otherwise destroy).
In this case we're limiting the voltage and the diode is reverse biased because that's how zener diodes are used. They break down (non-destructively) at a certain voltage.
In this case you have a device that has a limit of
+/-20V (see Vgs) between the source and the gate. So the zener id placed between the source and the gate in such a way that it will break down if the voltage exceeds something less than 20V. The series resistor limits the current and prevents the zener from being destroyed.
Using an 18 volt device is OK. It is probably a 5% part, so the breakdown voltage may be as high as 19V. But it's still less than 20V. If it was a 10% tolerance device then you'd be cutting things very fine.
Resqueline suggested a 16V part because 16 (or 17 or 18) leaves a comfortable margin, and 15V is typically what is suggested to turn these devices hard on.
The 1W rating is more than adequate, you could use a 400mW (or even less) device here.
edit: look
here. (same seller) they are 15 volt parts.