Yup. Unless the loot you're looking for is quest-rated. Treasure-hunting chests' loots are spawned at random, scaling with your current level.
When you are level 50 or higher you might find Daedric or Dragonbone stuff in even random chests; end-of-dungeon chests are guarantee to have high-tier stuff and/or beefy enchanted stuffs.
They do. For an example, as a lower level, you will find steel weapons to be quite common. As a higher level, say level 50, you will be able to find ebony weapons easily.