The Sick Man is a Story NPC that the player can interact with in one of the huts on the Frozen Village.
"Thank you so much! Please meet up with my son, I'm sure he will reward you."
You can collect the water In the secret cave, where the Ability Teacher is. One of the ice sickles in the cave drops water, Just go under it with the cup in your hand and wait, and it will eventually drop water into the cup.