The amount of entropy in a closed system is not allowed to decrease, but it is allowed to be constant. The amount of energy released by the phase shift is equal to the amount of energy absorbed by the object as heat.
Sure, but then the temperature of the object has to increase. And as its temperature increases, it has to stop condensing water - at the very least, once it reaches ~100C, it will instantly boil off any extra water that it condenses.