4th pillar contains the design of the first 3 pillars, just look at the 4 pillar to solve the puzzle, there are 4 possible solutions, the perfect RNG would be the 4th pillar to have the correct solution, as in this clip

The coins are optional (has to solve on the first attempt, without coins ())

the level of the key only influences the run in the idea of 100% of the clean vault, but as for solving the puzzle the type of the key interferes little, because there are several ways to solve, just find the fastest

Actually 100% would be a little more difficult to verify, but I imagine that for the run to have a higher degree of competitiveness, time would start when placing the key in the safe door and end when holding the chest of the old tributes

a run is possible to clear an Ancient Vault, for example, any% focus only on getting the chest of ancient tributes and 100% clearing all treasures from the vault