The Mall is an area directly accessed from the Nexus.

On the first map, Tokuto gets scared, drops an item in its liquid and runs away from you. After you trap him by changing the directions of the escalators using the levers, he will fall over and lose the item. It's the Warehouse Key.

Said Key grants access to the room behind the door on the rightmost side of the first floor. That is where the Mannequin Segment begins.

To get past the mannequins, you either have to be very cautious (stay away from them when the lights turn out; then run past), or use the Lamp Effect.

On the last map, there are mannequins surrounding a bed. Sleeping in it will cause the mannequins to move and almost kill you and you'll wake up.

Also on the first map of the Mall, to the left, there is a door you can enter. Take the elevator to the room above and you'll find the Valve there.

In the waiting room, the O-Man gives you the flute effect and supposedly inadvertendly locks the exit. Interacting with the E-Man and repeating the melody he sings will unlock the door again.