After some more digging/mapping, I found some more interesting results in my exploration of caverns. While some of this may be common knowledge, I'm finding things I'd not seen before and I think it's easier to just throw everything interesting, odd, or quirky I find here.

These two are exactly the same, with two slight alterations. The first one is 100 Openness, 0 Passage Density, the second the opposite, with respective values of 0 and 100.
What this means is that the overall general layout of the caverns is dependent upon the seed. Don't know if that was known or not before, but there lies the proof. This also means that I'll have to use different seeds instead of the same one to find out about how deep one cavern can actually be. Magma tubes like the one in the screenshots are also dependent upon the seed.
On the subject of how deep a cavern can be. Extrapolating the information that the actual layout of caverns is dependent on seed means I'll need to scour a variety of landscapes instead of just one. On the map I first began exploring, I've found that caverns themselves are typically 5 Z-levels deep, occasionally 6 levels, and rarely 7+ levels deep. I've so far only seen one 7 z-level deep layer and one 8 z-level deep layer.
However, there are a couple things to note that I passed by.
That opening, essentially a giant pit, extends from the second to third caverns. The full depth of that particular pit, from very top to very bottom, is 58 Z-levels.
There are also these interconnecting passageways that connect cavern layers to each other.
This is from an 8x8 embark, verifying another underground trait. Spoiler veins do indeed pierce the third cavern layer. There are four spoiler veins in that screenshot. Which suggests that those veins can go higher. Veins piercing the third cavern layer appears to be a fairly (un)common regularity. The three magma tubes being so close together is (incredibly?) rare.
WOOHOO!! Another !!SCIENCE!! Breakthrough!
I just came across another curious thing: demons change the underground landscape. The image above was with 0 titans, 0 demons and 0 night-time creatures.
Titans and night creatures do not appear to have an effect on terrain, on the surface or underground.