Low pressure and high pressure are not absolute. You find those pressures at any place. http://en.wikipedia.org/wiki/Atmospheric_pressure
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.
A low pressure area is caused by a drop in temperature in the atmosphere.
down
First understand that the boiling of water occurs when the energy of water molecules is equal to the vapour pressure... (i.e energy of water is equal to the external pressure due to the atmosphere)... above sea level the atmospheric pressure is lower hence low energy is required... hence water boil at low temperature...
Mars has an atmosphere with low air pressure which is mostly carbon dioxide.
Rain most often occurs with low pressure.
Low pressure systems often produce thunderstorms if the atmosphere is unstable enough.
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.
They form because of high and low pressure in the atmosphere.
mars
Mars has a low atmospheric pressure reading because there is a lighter atmosphere, which means less air, which means less weight or pressure.