Less pressure means a lower boiling point and more pressure means a higher boiling point. In general, the boiling point decreases 1 o C for each 1,000 ft increase in altitude. The temperature of a pot of boiling pot of water remains the same until the water boils away. Boiling is evaporation that occurs theroughout a liquid. Increasing the rate of heating will increase the rate of boiling, so evaporation will occur more rapidly.
Evaporation is a cooling process, so overall the temperature remains constant.
Heat is absorbed or released during a phase change as the latent heat of fusion or the latent heat of vaporization is absorbed or released. The temperature is constant during a phase change as all the energy goes into or comes our of potential energy. This is the definition of conduction. Relative humidity is a measure of how much water vapor is in the air compared to how much could be there at that temperature. Cool air will hold less water vapor than warm air, so cooling the air with no other changes will increase the relative humidity.