I don't know why was he taunting Maul when he was choking Satine, Maul was trying to lure him to the Dark Side so he would not kill Satine in short time. But after he was enraged by Obi Wan he decided to kill her to make him "share his pain". I admit I'm a bit frustrated when I read the book and watched this episode for these reasons. He gives me the impression that he loves Satine, but still couldn't totally break from the Jedi discipline. I'm not surprised of Maul and the Jedi Council's decision, but I had a bit hope in him, too bad, and that's why I don't like him..
Obiwan knew that Maul planned to use Satine against him. I think that is the reason why Obiwan got all preachy on Maul. It's like Obi wan was saying,
"Go ahead bro, I know you going to kill her anyways. Do it. Kill her. I will not let her death be in vain, I will hold to my beliefs. I will show you I am stronger by not begging, compromising on my principles, or becoming angry and breaking the code. There is no such thing as death, only the Force."
Sure Obiwan loved Satine, but for Obiwan and Maul, this was deeper, this was about religion.
Obiwan did not shed a single tear for Satine, do to so would of proved Maul right. That peace is a lie, there is emotion. To get emotional, would of dishonored the Jedi, Satine, and Obiwan.