A polarizer can make some reflections disappear or, if rotated 90 degrees, it can make the reflections stronger. In general, transparent materials, like window glass, water and even air, affect the polarization of reflections, but metallic reflectors do not. So, in answer to your questions:
- Depending on rotation of the filter, it can increase or decrease the "wet look".
- It depends on the filter orientation if glass reflections are eliminated or exaggerated.
- It should not change the shape of lights.
- A good, clean filter should not create much extra glare or flare on lights.
- It can remove glare from still water, but is less effective on ripples.
- It can darken and intensify the color of the sky at 90 degrees from the sun on a clear day. At night, it might have the same effect for moonlit scenes.
Why not buy an inexpensive polarizer for your camera and experiment? Keep in mind that it decreases light by about two f-stops, so can increase noise in a digital camera or induce reciprocity failure with emulsion photos.