How can I use the "Windows Live Call Button" on my headphone to answer a call with Skype?
There is a small utility created by Jonathan Kay named Skype Call Button, which can be used in this purpose. It runs in background, and catches the button press events, and you can configure what it will do:
It integrates with Skype (which will ask you if you authorize this program), so that you can answer an incoming call by pressing the button.