Shaking Hands With the Opposite Gender

Question

At some point, I was told (or taught) that the reason why a man cannot shake a womans hand was because of niddah. However, if the woman is at the age where niddah no longer applies, or the woman is not jewish then it was okay. 1. Does this have any basis in halacha? 2. What is the halacha, and what is the basis for it? 3. What is the halacha regarding a jewish woman shaking a non jewish mans hand? Thanks Again Note: Being introduced to your website has started me thinking again. (Perhaps too much.)