When temperature of water in earthen pot is less than temperature outside, will earthen vessel help in maintaining the temperature of water inside constant (or) will it help by decreasing the temperature inside?
I think it only helps in maintaining temperature of water inside vessel constant. If you take the same water in some steel vessel, as it is a better conductor, it will absorb heat from surroundings and transfer heat to water inside making it hotter. In case of earthen vessel, the water in pores doesn't decrease the temperature of the water inside, it only helps in maintaining temperature if we follow rules of heat transfer.
The the presence of the pores will enable water to reach the outer surface of vessel, where it can evaporate. This will cool the outer surface.
This will not cool the vessel. As the temperature outside is more than the temperature inside the vessel, it will will take heat from outside and evaporates. This will help in maintaining the temperature of water inside but doesn't cool the water inside. It will not allow the heat to flow from outside to inside.
Why should it not reduce the temperature of the water? Start with water at room temperature and some of the energy for evaporation will come from the water inside - reducing the temperature. Why do people die of exposure if that doesn't happen?
Yes that works to cool the water inside; and it's perhaps the main reason for its use in places without electricity. It's the simplest fridge in the world.The the presence of the pores will enable water to reach the outer surface of vessel, where it can evaporate. This will cool the outer surface.