I asked the Grey Lady about the secret passageway; she said it's been here as long as she has but the last person to use it was a boy called Cicero about 150 years ago. I assume he must have put a preservation spell on the room for it to be in the good condition it is now.
Chaeyz and Jenyae and I will be going down together in a few hours, and I suspect the cat will too. He needs a name, even though I don't know if he plans to stick around.
ETA: Chaeyz suggested I call the cat Cicero, after the boy who used the room. Minda looked obliquely pleased when she heard this and began quoting some ancient Muggle writer, so I guess Cicero it is.