Dreamscape
Faye's dreamscape will be structured in a series of three levels; each subsequent level represents a deeper aspect of her psyche. (If you've seen Inception, it's pretty much similar to that structure.) By the time one reaches the innermost level, they could potentially come away with a knowledge of the parts of her mind that she likes to keep carefully hidden and locked away. Memories, fears, vulnerabilities.
Level 1: You find yourself on a glass elevator, which will eventually lead you to a 21st-century casino. (Which also happens to be the very same casino where she met Spike and Jet for the first time. The place has more personal significance than she would like to admit.) This is Faye in her natural element, and represents the most basic and superficial understanding of her personality and dominant behaviors. As you pass through the slots and card tables, you may or may not see her trying her luck, or trying to cheat/swindle some poor soul out of his money. At this point, nothing seems particularly out of the ordinary; even the use of woolongs as a currency is perfectly natural to you. The rules here are similar to the rules of real life: you can win big, or lose big. But this won't last forever, because eventually you'll progress to...
Level 2: The Bebop. Though a hunk of junk tin can that isn't exactly anyone's idea of fine living conditions, this is what became a home to her over the course of her canon. One of the more notable locations on the ship is the living room, consisting of the world's ugliest yellow couch, which is where, canonically, the ship's inhabitants spend a lot of their time. Here, you'll probably find a lunkhead Spike asleep on the couch (feel free to hit him. pissing him off is fun!), Jet wandering by on his way to go do whatever he does with his bonsai, Ed... being Ed, accompanied by Ein. These guys are practically family to Faye, and are thus going to figure prominently in this dream, even if you may or may not be able to interact with them.
Passing by the bathroom with the shower that doesn't work about 85% of the time, you'll eventually reach Faye's room. It's pretty standard as far as spaceship quarters go, a small room with metal walls, the only real visible features being a bed and a television. On the television plays one tape on infinite loop: the video message that Faye recorded to herself as a child. The only tangible evidence from a past that now only exists in recently resurfaced memories. If you watch this tape for long enough, you may find yourself somewhere else entirely, leading you to...
Level 3: Level 3 is a cold, empty space, full of locked doors and echoes. It's mysterious and surreal, completely devoid of color and life, like the baroque room from 2001: A Space Odyssey, only full of endless hallways lined with said locked doors that stem from an open center room. Images are projected all over the walls, the ceiling, everywhere; the same images shown on the beta tape. This is the deepest part of her mind, where all of Faye's deepest secrets are locked away tightly. Opening the doors will require some force and/or determination. Who knows what will happen if you try.
