I'll answer your questions backwards because the last one is in my head freshest.

You should keep counting until you get to a dream. You aren't supposed to fall asleep (your body is) your mind stays awake.

Weird things don't invoke lucidity because the logical part of the brain is for the most part, turned off.

Spinning and rubbing hands are designed to keep you in the dream that you are in, not create a false awakening. The best way to invoke a false awakening is to simply close your eyes. This can also cause a real awakening though.

I recommend a different method for stabilization. Forget stabilizing your dream, let yourself wake up, but don't move a muscle. You will immediately get sucked back into your dream and have a DEILD. I use this method all the time.