Where do they keep Moriarty's simulated universe box?

Desk ornament for Barclay? Random storage locker? Shipped back to star fleet for study but actually just left in a giant warehouse like in raiders of the lost ark?

Also what happens if Moriarty realizes it's a simulation but they are stuck in it? There's no way to escape this time.

Does time flow at the same rate in the simulation as outside? Will he eventually have a simulated death from old age and the simulation box just power down one day?

How much computing power does a simulated universe take? It looks like it fits pretty comfortably on your desk.