Yeah you need the lock washer on there to make sure the nut doesn't take a vacation. It goes under the nut then you bend it over. You can test the sensor yourself though. take an ohm meter, and connect it to the wires. Then take something metal and it should cause a change in the reading. Not sure what the resistance should be but a service manual should tell you.
That lock washer is important yes, but what about that other washer? It's a pretty big washer...
As for testing the SS.The manual tells me i need power to test it like that, but it wants a little harness tool that makes it way easier. I can't tell if i'm ever doing it right. The guy at the dealership has the tool i'm assuming and is only gonna charge me like ten bucks. I'll just bring my pile of speed sensors down and have em check it out.