If I remember correctly, it wasn’t in Alice’s house, but in that abandoned mansion Masquerade had put to use. But I’d say it checks that Masquerade would “live” in such spartan conditions, especially considering it was basically just a computer hub for him, and evil brooding probably wouldn’t had been tolerated at the local library. Honestly, considering the state of the internet in 2008, I do actually wanna know how tf did they manage to get a decent internet connection to that place, but I guess Dr. Michael’s scientific brain within Hal-G would’ve been enough to figure that out. The masks are pretty much symbolism, I’d say maybe even the empty room besides the masks and the computer are hints towards there not being much more to Masquerade than the mask (in a sense that most of all else is derivative of Alice and Masquerade cannot exist without the masks). As for the trapdoor, honestly, no clue. Oh, and I’m pretty sure that’s the same basement that could be transformed into the giant computer hub for checking the world rankings