The water seems to be recycled through a filtration/recycling system on the ship. The plumbing seems to still be working, but there's only so much water left. Any storage of water seems to be running low, that you can see.

No such diagrams, necessarily, but there is plenty of indication that there has to be a storage facility somewhere, by inference. 500-600 people clearly could fit in this room, so where's all the food?

Any scent of food or food-like substances . . . maybe the odd smell of vegetation, would lead him directly to a locked door.