Thank you for having such a close read! I wanted to make it so that a DM has everything they need to run the one shot - and yes, the various PCs all have items/skills that explicitly help with specific environmental challenges.
Correct, they start off with almost no items and have to scavenge things (although the Houri was able to sneak her hair pins past the Jade Order). Re: rooms A3-5, they will definitely make it harder to flee the site but I would advise DMs to be open to creative player solutions. If you look at the map, there's a number of ways in which the NPCs could by-pass the blockages. They don't HAVE to resolve the Lament (this is also why I gave the pregens conflicting "wants").
Funny that you picked up on the question around the Houri's skills. I purposefully left that a little ambigous, so that DMs can decide how they want to play it. The powers would certainly work on any human/humanoids. The rest is up to the DM.