You know what?? I doubt that too many would survive a WW3. Probably most of the population will die. I don't think we can possibly know who will win (if there will be someone left). Little do we know about the secret war stuff the goes around.....
Oh no you can speculate the likely outcome of a mutual nuclear annihilation. There is always one survivor in war. i doubt its a zero zum game.
Not if Earth becomes uninhabitable. Once deployed by someone waging a war, it is unwise to think that extremists would consider such irrelevant facts as how many fusion bombs does it take to destroy the climate.
I'm going to play the 'haha, you MUST be joking". A third world war would spell the extinction of the human race. Even if you remove the threat of Nuclear Annihilation, biological and chemical weapons could wreck unimaginable damage. The age of Global wars is over, since our World could be destroyed in a instant with the bush of a button.