Incorrect. Climbing Everest is more about high altitude conditioning, stamina and mental toughness as this 73 year old Japanese woman demonstrated.
73-year-old becomes oldest woman to climb Mount Everest - CNN.com
Exactly. One of the main problems with climbing Everest isn't so much the strength required, but rather how well your body can handle an oxygen lacking environment. Ever been up at altitude? It kinda sucks because you get worn out a lot quicker than you would if you were at a lower altitude. Easiest way for an American to demonstrate that for themselves? Go to Colorado and either drive or ride the trolley to the top of Pike's Peak. Even at only HALF the altitude of Everest, it's pretty hard work running around at the top.
And lighting a cigarette with a Bic lighter is damn near impossible.