This is a nice "why does my cat... ??" site.
http://www.xmission.com/~emailbox/whycat.htm
Interesting, I always wondered about the "little bites" several of our cats will give us when we're patting them.
As far as the running water, we have several cats that insisted on drinking at the sink. We solved it with this,
We got it online for about $50. They all love it and are all drinking a lot more water, and that is a good thing.
Made by an company called DrinkWell.