Relic 1 (A Father's Sword)
In the location, where you push down the truck, in the main storyline, and walk over to the chamber below. From there, you can get to the chamber right above the camp, where there is a chest with the relic. Examine the broken tip of the sword.
You cannot miss it. It is right next to the campfire (in the Pantheon Corridor camp).
Chest 1 (Crafting tools)
In the big chamber, on the left in the recess.
Chest 2 (Element of the bolt-action rifle)
In the same chamber as the above chest - before the chamber with canisters in it and an explosive barrel, on the left, there is a path up and that is where the chest is. You need a lockpick.
Chest with coins 1
At the opposite end of the chamber, where you find the monolith.
Chest with coins 2
In the corridor, in front of the entrance to the big chamber.
Chest with coins 3
In the corridor below. The path down is in the big chamber, over the wall of ice.