Low pressure and high pressure are not absolute. You find those pressures at any place. http://en.wikipedia.org/wiki/Atmospheric_pressure
Yes, Mars has a very thin atmosphere that results in low air pressure compared to Earth. The average surface pressure on Mars is about 0.6% of Earth's air pressure at sea level.
It can do. Winds in the atmosphere cause waves. Also the low pressure in the centre of a depression can cause a elevation in sea level called a storm surge.
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The air pressure in the mesosphere is low compared to the pressure at lower altitudes. This is because the mesosphere is located at an altitude where the density of the atmosphere is much lower, resulting in lower air pressure.
Air travels from high to low pressure in the atmosphere during flight through the process of air movement known as wind. Wind is created by the pressure differences between high and low pressure systems, causing air to move from areas of high pressure to areas of low pressure. This movement of air helps to balance out the pressure differences in the atmosphere.
Mars has an atmosphere with low air pressure which is mostly carbon dioxide.
Rain most often occurs with low pressure.
Mars
Atmospheric pressure is caused by the weight of the air in the earths atmosphere that is above you. At sea level this pressure is said to be 1 bar or one atmosphere. Now, as you go up a mountain there is less air above you and thus the atmospheric pressure is less and the pressure you experience because of your altitude is said to be your local atmospheric pressure. However, the earths atmosphere is heated by the sun and moves in eddies to the poles where it is cooled and flows back to the equator - this is called the weather. When you have hot air above you it is less heavy than cold air so, as the atmosphere blows over you, the pressure of the air changes and you can work out if the air above you is hot or cold by comparing the measure you measure against your local atmospheric pressure.
The pressure in the mesosphere is very low, around 0.1 millibars at the bottom of the mesosphere and decreasing even further with altitude. This low pressure is due to the thinning of the atmosphere at higher altitudes in the Earth's atmosphere.
Pressure differences in Earth's atmosphere create areas of high and low pressure. Air flows from high pressure to low pressure, creating wind. The greater the pressure difference between two areas, the stronger the resulting winds will be.
Air tends to flow from areas of high pressure to areas of low pressure. This movement occurs in an attempt to equalize pressure differences in the atmosphere.