How would the pressure and temperature at 100 m below sea level affect the speed of the air molecules in your lungs compared to their speed at sea level?

Answer: Air molecule move faster

Pressure, temperature, and volume is related to each other. If you compare sea level and 100m below sea level, 100m below sea level will have more pressure. Pressure is a force caused by molecule impact, so increased pressure means faster molecule speed. More pressure can be translated into less volume which means the air volume in the lung is decreased (with same molecule count).