1: The lens hood does not constrict the light coming from the subject, the lens hood prevents light from off to the side, outside the area you are photographing, from causing glare on the front of the lens.
2: A polarizing lens has several things it can do, all of which are difficult or impossible to do in post processing. Light has polarity, "A and B" or "+ and -" or something like that, and the CPL will filter out one or the other polarity.
As an example, light coming from the sun is all the same polarity. When the light is reflected or refracted it changes polarity. So if you are looking at the surface of a still pond of water you can use the CPL to either enhance the reflection you see in the surface of the water or to reduce the reflection so you see more of what is under the surface. The CPL also increases contrast and can make blue skies look really, really blue.
3: Any of the above. Some lenses will do this especially at their widest focal length and widest aperture. Sometimes a lens hood can cause a little of this. Sometimes people add it for artistic effect.