Part of it makes sense but not all of it.
This is not entirely accurate. When atmospheric pressure drops, the partial pressure of oxygen drops accordingly. The partial pressure of oxygen is 0.21 times the amospheric pressure. At 16k ft this would be 0.21 x 0.5 atm=0.1 atm O2. The concentration of oxygen in your blood must be maintained by your body at a constant level regardless of the partial pressure in your lungs. At altitude, you breath in fewer molecules of O2 with each breath (and transfer to blood is less efficient too), and hence you must take more breaths in a given amount of time to saturate the hemoglobin in your blood.
Yes. The pressure increases by 1 atm for every 33 ft of water, or decreases by half for every 16,000 ft of altitude.
Earth's rotation accounts for its distorted shape. The centripetal force causes the earth to bulge. The atmosphere bulges proportional to the rest of the globe. I know that storms can rise to 40k ft at the equator, but the cloud tops seldom exceed 20,000 ft in the actic, but this may have more to do with temperature than pressure. The Nova website on Everest puts the pressure at the summit 3,000 ft lower than it would be if it were at the same latitude as Denali. Some of this extra pressure comes not from the latitude effect but because Everest is located at the center of a continental land mass, whereas Denali is at the margin of one. High pressure systems center on big land masses with highest pressure towards the center of the continent.
Couldn't be Tom Hornbein. He's been climbing for a lot longer than that.