No. The sensor is made of discrete photosites. When you reduce the resolution, the RAW data is still the same except that it is downsampled when rendered into a JPEG. So the pixels and amout of area of each photosite remains the same and is shot and read noise at each photosite.
Should you reduce the resolution you are also implicitly reducing the amount of dynamic-range in the image since a JPEG is 8-bit-per-component while a RAW file can have 12 or 14 bits, depending on the particular camera.
Yes. The apparent noise get reduced since if you are looking at 100% magnification, what you see is a smaller image with pixels binned together which averages out noise. Should you print at the same size though, the noise you see will be largely t he same though.