Where did people go to the washroom in castles in the medieval times?

Answer 1

There were no wash rooms in medieval castles. People washed in their bed chambers, if they washed at all, from containers of water brought by their servants. Castles were never intended for anyone to live their comfortably or for long periods, which is why knights mainly lived at their manors.

Perhaps you meant to ask about latrines, which were usually built into the thickness of a wall, with access from the bed chamber or from the main hall. These had a narrow window without glass and a wooden plank with a hole in the centre - this was built to project out from the wall below so that body waste dropped down to land in a cesspit at the base of the wall (as at Dover castle) or into the moat (which eventually became a disgusting sewer).

Answer 2

The streets, rivers, backyards, and into pots. Eventually, to make gun powder they collected urine because when dried it contains salt peter, but that came much later closer to the 1400's.