A basement is a large room under the ground. A dungeon is a room under the ground.
A basement A bunker A cellar A cave A cavern
A large room is commonly referred to as a hall or a auditorium.
It is called a basement
An undercroft is a large cellar like room. Typically at ground level or just under. Often it would have the Refectory on the first floor.
a salon
Rood
The space under a staircase is called a spandrel.
The room under the roof is called an "Attic".
A basement...
It would be called the "ATTIC".
They could be called a 'Sun Room', or 'Solarium' or Boom Boom room
because lava under the ground is rising causeing less room for the trees to grow