To test a zener you need a variable power supply with a setting that enables very low current. I have blown zeners using too much current. You can put the zener between your fingers to see if it heats up during the test.
If you use a 12 V power supply, you need to restrict current through zener with a series large value resistor.
If the zener is mounted between the gate (cathode of zener) and source (Ground, Anode of zener) it is a protection diode and the comments as to the value are appropriate.
However, if it is a protection diode, the FETs should work without the diode, unless they are blown again.
Wally