I'm back with more "finishing basement" questions.

This weekend, I wired my bathroom. This is 20 amp service with 12 ga wire. For the bath fan/light, the power source came into the switch box (1 box, 2 switches) on a 12/2 wire. From there, power goes up to the light/fan on a 12/3 wire. Red goes to the fan, black goes to the light, white connects to two white wires in the light/fan unit, and ground connects to the green wire in the light/fan.

The light works, the fan does not. My hunch: for the ground wires, I tied the power source ground with the ground that goes to the light, then pig-tailed it and connected it to the ground screw on the LIGHT switch. Assuming everything else is wired correctly (which I haven't checked, but I will tomorrow), would my failure to connect the ground to the FAN switch cause the fan to not work?

2nd question:

All the diagrams in my wiring book say that in the box, I should connect the ground to the box as well as the outlet or switch that's in the box. However, I'm using plastic boxes and there's no place to connect the ground wire. So the book says in that case, ground it to the screw that goes into the outlet box. What a pain. Is this necessary? Are there any alternatives?

Thanks so much in advance...
Trip