The idea is neat but there is some confusion for me gameplay wise.
That you have so many questions about its mechanics already tells me that it is not well designed.
Are you supposed to be able to survive the monster by jumping into those cabinets?
To survive the monster there are several mechanics such as closing doors behind you, hiding in closets, running, to try to take distance and mislead it.
Sometimes in hallways there is literally no way forward because of the traps. Sometimes one of those side-pushers pop up right next to a spike spot, is it meant to be like that?
All the elements of the level are procedurally generated, the traps as well. But they can be avoided by taking alternate paths or sprinting.
Is there only one way to get to the next level (the stairs)?
The objective of each level is to find the door to the next floor (indicated at the beginning of the level with a graphic). The stairs are shortcuts within the level, these shortcuts do not have any light source, they are dangerous and contain rewards.
Also, is it fully randomly generated? I see ghost players and I assume they function as in Dark Souls. Is their movement actually synced with the seed for the level I'm playing on?
That's how it is. They are generated from a seed. The echoes of other players who passed through that level are recorded, their presence gives us clues about the path and if they died, we can find the corpse and loot it.
I just saw your 4 attempts on the server
the other players will see them if they play the same game. Every time we play a new game there is a 50% probability of starting one that no one has visited and a 50% chance that it has already been visited and contains echoes from other players.
I see that I am not transmitting the objective, the rules and the mechanics well. What a mess