A polarizer helps reduce or eliminate reflections which can cause blown out areas of your image. Another effect a polarizer can create is more saturated colors and can give a blue sky a great looking gradient. I mostly use mine for shooting skiing. I will also be using it a lot for shooting wakeboarding this summer in hopes that it will decrease reflections from the water.
I don't think a polarizer will be of any help in low light. Polarizers tend to block a little bit of light which would not be ideal for that situation.
^ Yes, there is quite a bit of room under there, I've had no problems with 2, and would think there is room for at least one more. Might get vignetting before you hit it.