Actually, i think in the 1st situation:
1. Go to the highest point you can reach in Kakariko. This is the top of the highest building on the north side. I'm not sure if you actually need to be on top of it, or level with the front entrance of it...but you'll figure it out. Walk to the edge closest to the entrance to death mountain. You should be able to look down and see the chest you were referring to and you should be able to "barely" jump off the edge of the building and land on the platform its on and open it.