I doubt the core would heat the bottom levels much more than the top. I'm no thermodynamics major, but I think the distance would need to be much greater, unless it's sitting above magma (but it isn't, it's a lake). On the other hand, if the lake is heated enough, the hot rising air could warm the lower levels without doing much to the upper (though the perimiter of all levels under the ceiling (I think that was 3+) would be warmed slightly, though not as much as the smaller bottom levels.
I've seen snow in Hydlaa, so unless that is an idiosyncrasy, it can reach freezing. But speaking of snow, there's another temperature problem. In reality, snow occurs because water vapor freezes when it rises . The extra heat from the sun doesn't occur until very high, past the layers that block much of the radiation. The ground is warm because the ground absorbs the heat from the sun and then radiates it back out gradually, but up in the air there is no ground, so you only get the first dose. In Yliakum, rising means getting closer to the crystal. Unless the crystal is many many miles above, so that an atmosphere like earth's forms, the water wouldn't freeze and form snow. It would rise, then get hotter. I guess it would either collect, escape upward through cracks, or condense on the walls and run back down along the edges. It would run along towards the crystal, but it would get vaporized again, so only the vapor that winds up by the sides could condense and fall.
So maybe the ceiling that isn't near the center by the crystal is cool enough to condense the water and allow "rain" to drip from the small stalactites and bumps, or sheet along the sides of the walls. If it's cold enough, it could freeze the water into snow. That could be possible, considering how wide Yliakum is, and that the cieling wouldn't get the full burst of the crystal, just part (like at winter, when the sun is at an angle). For example, look at the ceiling away from the ceiling light. It's probably a little darker than the rest of the room, especially if the room is wide with a bumpy ceiling and a close floor.
For the lower levels, they may be far enough away for some kind of mid-air condensation to occure. The faces of the cliffs probably don't get as much light either, so they'd be a little cooler and not radiate as much heat into the air, and in the middle where there is no land, it would be cooler. If there is some kind of heat from below to warm up the bottom, the middle air would be even more likely to cool enough for condensation because the below heat would never pass directly through the air like the crystal's does. So it would just be the heat radiated from the ground.
As for light, there is another possible source. Glowing objects. This is all underground after all, so maybe there are phosphorescent animals in the tunnels or lakes. They could possibly be processed into glowing paint, or even kept as pets. Then there is the possibility for artificial glowing things, wither by science or magic.
The glowing items made by magic don't have to be expensive. They would for random George to go and learn magic to make it, but they may be able to buy them cheaper. Look at a newspaper. How much do you suppose a printing press costs? Much more than the paper, that's for sure. The cost of learning the magic is a one-time cost. What the consumer worries about is the cost of ingredients and time to make the "globe". The globe-maker will eventually pay off his investment and start earning profits, as long as he sells them for more than the expense of actually making one. That isn't to say they'd be cheap, but they may be affordable.
Another thing about windows: Have you seen that funky area in Hydlaa with the one-way walls? Something similar could be done to make entire walls of your house transparent. However, that would probably be very expensive, even if some wizard mass-produced them. It's a remote possibility, but I thought I'd mention it.
