How did they redesign the King's Storeroom into the Room of Ancient Warriors, and not only did they remove the ladders but did they also move the wall of The Jester's Court forward?
They removed the ladder from the Jester's Court, but they probably left the part of the ladder that intruded up through the floor of the King's Storeroom, shielding them with the Ancient Warrior armors. The armors are pretty far forward, and they are staggered in a way that makes me believe it was the only way to give the temple guard room to maneuver around the ladder in the back to access the armors, while not having to go through the trouble of taking out the remains of the ladder. But I think that the pedestals on which the clay pots stood were re-purposed for the Season Three King's Storeroom, but the ladders would have still been in the way.
The Jester's Court wall doesn't seem to be moved forward, in my opinion. The lighting just got a bit darker, and they got rid of the ladder and laugh track when the door was activated, but that's all they changed in that room.
Did they repaint the Room of the Mandarin Hand to become The Chamber Of Sacred Markers?
They obviously got rid of the Mandarin hand and then built up the center wall that enclosed the ladder leading to the King's Storeroom. As far as repainting goes, it was either that, or they painted directly on some other surface, such as Masonite or something of that nature, and then nailed/screwed (or some other means of attachment) that on top of the preexisting wall.