[1] http://www.amazon.com/Svante-P%C3%A4%C3%A4bo/e/B00GJ9XR7O/
"The Neanderthals Rediscovered", by Papagianni and Morse, has a good chronology of the species based on what is known to date.
A human that has one Neanderthal gene is not a Neanderthal. Therefore, Neanderthals are still extinct.
There's one other thing that I think people living in the Himalayas have, myself included, that helps and that is proportionately humongous lungs. This is probably evolution at work over the course of centuries.
That's funny. I had to Google it because I never heard about that before, but apparently it's extremely common!
According to Wikipedia this trait is common not only on asians but also native americans, so it predates Genghis Khan.
Extinct? Hmmm. Get over it we are partly neanderthals, denisovans and so on.
Edit: Apologies to the downvoter, I should have substantiated that claim. I have added a source.
[1] http://www.infoplease.com/encyclopedia/society/neanderthal-m...