The North Pole is essentially at sea level these days, at least in summer when it is often ice-free.
The South Pole lies towards the centre of the Antarctic Continent, and is at an altitude of about 9 000 metres. So it is much colder, and the air is much 'thinner'. The relative humidity is very low, for there is essentially no water vapour in the air. For this reason, the Antarctic Continent is largely a desert.
Booty
yes
The earth is slightly flattened at the poles. This has the effect of lowering the surface and raising the weight of air above.
It goes south and new hot air comes up to the poles to be frozen and pushed back down.
it is because air sinks at the poles
Generally the poles are cold places, receiving Sunlight at a low angle or no Sun at all. This means the air above the poles tends to be cooler than the rest of the planet. Cold air is dense so the pressure of the air at the poles tends to be higher than the rest of the planet. Thus air (cold air) tends to flow away from the polar regions along the Earth's surface to be replaced by light warmer air flowing into the poles at a higher level (this air then cools). There is therefore a general flow of warm air north and south towards the poles from the equator and a flow of cold air from the poles towards the equator. This flow of air spreads out the heat from the Sun, warming the poles and cooling the tropics. In detail this overall flow is restricted by the thickness of Earth's atmosphere and several flow cells form to complete the chain causing Earth's climatic zones.
Away from the poles because the air near Earths surface is warm.
The reason the tropopause is lower above the poles than the equator is... The time it takes air to cool. The surface air-temperature at the equator is much higher than at the poles, meaning that the air rises further to reach the equilibrium required at the tropopause. Likewise, the air at the poles is cooler, and does not require as much room to rise.
low pressure and high pressure
Think of the air at the Equator as a column. If you heat it, the air in the column expands and rises, cooling as it does so. As the column gets taller, at altitude you have relatively higher pressure, and the air flows out towards a lower pressure area. When the air flows out from the top of the column, it leaves lower pressure at the surface. The opposite happens at the poles where the air is cold and dense. The column is shorter and heavier than the column at the Equator. The pressure is lower at altitude and so the high pressure air from the Equator flows there. Adding air to the top of the polar column raises the surface pressure and the air flows from there to a lower pressure area at the equator. So you get a circulation, out from the Equator to the poles at high level, and in towards the Equator at lower level. The air that left the Equator was warm when it was on the surface at the Equator, but by the time it has risen 40,000-50,000 feet and traveled several thousand miles at high altitude, it is no longer warm. The rotation of the earth and the roughness of the terrain affect the flow greatly, and the air at the surface tends to turn to the right causing rotating areas of high and low pressure.
From west to east
Yes the surface pressure is caused by the weight of the vertical column of air above a surface.