seeing it in the flesh will make it all clear. I think a trip to a good camera shop is a great idea. its hard to visualize how this stuff works.
You don't have to remove the UV filter to put on the CP. If you want, the UV filter should have its own threads in the front, just like the lens did (same size too). Stacking is ok. I would actually put the CP behind with UV filter because the UV will protect the polarizer from scratches, etc..
Here's a stock photo of a polarizer. See how there is a ribbed section and a smooth section on the side of the filter? These are separate pieces (though they are attached together). You thread the filter on an tighten it down. At that point the smooth piece is fixed in place and you grab the ribbed portion and rotate it. Fingers never go on the filter glass. rotating the ribbed portion relative to the fixed (smooth) portion is what lets the polarizer do its magic.
