Yes indeed; it's particularly odd to see in the eyes, where the milky blankness we're used to seeing in marble statues actually used to have a painted iris and pupil on them.

It's hard to know whether it's just a bias from a life spent associating unpainted statues with high culture, but I much prefer them unpainted.

Yep, here are some possible examples of unpainted and painted (found by Infrared and X-ray spectroscopy):

http://io9.com/5616498/ultraviolet-light-reveals-how-ancient...

It's true. Greek, Roman and other works were often painted bright colors to give them the appearance of life, but have either faded with the years, or removed for political reasons. We still have beautiful and colorful egyptian sarcophagi, which gives an insight on what they may have looked like. On that note, the pyramids themselves were covered in limestone (if I remember correctly) and painted with bright and colorful markings. The reflective material would look as if each pyramid was a beam of light to the heavens during the day. Unfortunately, that's all been stolen, eroded or destroyed.