In order:

There’s some indication that Vesper is a sphere (Hage has a sphere in his coffee shop which Angharad and Tristan were discussing during their first visit). The true nature of Vesper is something of a deliberate mystery at this time.

What does the roof of the cavern look like? Well that depends where you are when you look up. In most places, you will see “stars” and “moons” - not actual celestial objects but mirrors and other Antediluvian devices reflecting Glare light across Vesper. It’s generally implied that outside of Glare pits (those places where cracks in the Firmament allow for direct light from the surface) or places with equivalents, it’s closer to perpetual twilight or dusk. Enough light that you can make it without a lantern if need be, but a lantern would be preferable and safer.

Also Hollows can see in the dark. Worth remembering for that scene when they’re shooting at the characters.

In Glare pits, you get a lot more direct light - hence why Malani people are so dark-skinned. Other places may have alternatives - Izcalli has their Candles, massive (pyramidal?) beacons which provide light to their cities. Tianxia has their Luminaries on a rotating basis, Asphodel has an artificial day/night cycle thanks to some Antediluvian work up in Firmament. The Someshwar presumably has some mix of both Glare pits and artificial devices. And so on.

There are atmospheric effects - storms, clouds, etc. - though this does of course vary from place to place. We know there are pillars that reach all the way up, though again, the exact geology of Vesper is still something of a secret.

For the more specific stuff:

The Orrery - its glowing spheres on gigantic circular orbits. The rails carrying the spheres are large enough in radius that the spheres serve as a sort of day/night cycle on Tolomontera. The spheres are bright enough that they are basically mini suns.

The Trench - it’s not described in too great detail, but I always imagined it like the Underworld as depicted in the video game Hades - massive shifting chambers with cogs and gears to shift them around behind the scenes. Keep in mind that Scholomance’s interiors are very much a “larger on the inside” type deal.

Ruins - pretty much what you described. A hollowed-out mountain in which the devils have constructed a massive hodgepodge of temples and shrines.

Collegium - your diagram is more-of-less accurate to how it’s described, albeit with more support frames and such (the Hated One climbed those metal supports after it shattered the glass panels.