Kosher: Meat and Milk

I would like to better understand the reason for the Jewish practice of waiting six hours after eating meat before eating milk products. Where is this in the Torah? Is eating them close together considered like cooking them together, which is very hard for me to digest (pardon the pun)?

Kosher Kitchen

We are becoming more observant and considering becoming kosher. If we decide to do so, what process, if any, is available to make our dishes kosher, or must we get all new dishes?

Kosher: Meat and Milk

I have always had trouble understanding the prohibition of consuming meat together with milk. I can understand if there are certain animals that their consumption has a negative effect on a person. But if an animal is kosher by itself, and the milk is kosher, why should they be forbidden if they’re together?

Kosher Loopholes?

I was with family in New York who are very Orthodox and strictly kosher, so I was very surprised by what I saw happen in their house. They were cooking meat on the stove and one of the children accidentally dripped a couple drops of their ice cream cone into the pot, which I would have thought would have made the whole thing non-kosher. But my cousin, who is very strict about everything and studies Torah every day, came home and said it’s ok because not enough dripped in to render the meat not kosher. I didn’t want to say anything, but it seemed very self-serving; how could he decide that it’s “not enough” to make it non-kosher?! If G-d said meat and milk is treif, why would this not be treif?! Am I missing something?
I would appreciate your answer because this has really been troubling me; in my mind it calls into question their integrity in all they do.