The way I got it explained was that it's the heart that can't handle the stress the lack of repeatedly not getting enough oxygen causes. The damage it has done to my heart before I got diagnosed is also not reversible, the goal is to not let it get worse, stay healthy, etc. I've been a patient for over 8 years, lost a lot of weight, didn't help, so for me it's imperative that I can see my own data and grasp what is going on. As to answer your question, yes and no, you don't really wake up but your deep sleep gets interrupted which causes you never to feel rested, especially if you have a severe case, like more than 30 AHI per hour (like me).
I'm very curious about the answer to this. I would expect the answer to be "yes." The current fad in alternative health groups is to tape your mouth shut while sleeping in order to improve sleep quality. I haven't heard of anyone dying yet even though it sounds pretty scary.