The key to the chest is on the ground level of the house, on a shelf on the wall just north of the hole in the floor.
screenshotThere are no capes. Perhaps they will make it into DD2 (this was suggested for Beyond Divinity, but did not get implemented).
Can't you just leave the practice area to get away from the instructor? IIRC there should be a brief conversation when you beat him, you get a level of a skill (either Augment Defense or Augment Damage), some experience and that should be it.