Weworance, I'll take a stab at the questions you raised, but please note that I am answering based on what I have read, not what I have personally done.
As I understand it, the contacts are indeed simply tungsten. According to one book, they are available for purchase ... but if so, I have no idea where. I had thought about, if I ever try to make my own points, getting a 1/8" TIG electrode and cutting it to size.
As far as machining the tungsten, I don't think carbide will cut it (if you will forgive the pun). You can grind a TIG electrode using an aluminum oxide wheel, but not quickly; diamond is the "correct" choice. If I were to attempt this, I would think about getting a thin diamond cutoff wheel to cut it, and then hone it to size on a diamond "stone."
I don't think there is any heat treatment needed (or even possible??). The book that I referenced above talks about silver-soldering the tungsten in place.