You can leave the UV in place, but there is no advantage to doing so, and it might reduce the quality of the final shot be being there (there are endless discussions on the various forums on the merits of leaving a UV on lenses or not).
Personally I always take the UV off when I fit a polariser on - in part that is to avoid vignetting - where the corners of the final shot are darkened by the shadow from the filter rim. I have spent the extra to get a specially thin polariser, so to stack it with a UV seems the wrong thing to do
A CPL will (as a side effect) drop the light by (I think) 2 stops, but the cameras exposure meeter should automatically adjust for this and just mean a larger aperture / slower shutter to compensate.
Note: Rob replied while I was typing, but thought I might as well post anyway, to confirm what he said:-)