Minecraft – Do spawners work in the Nether

The same rules apply to Monster Spawners as to the natural spawning of the mob in question, with two exceptions:

1. Ordinarily, hostile mobs will never spawn next to the player, but with spawners they can.
2. Natural spawns require ground underneath the mob, but Monster Spawners can create monsters in midair.

It is also important to understand the effect of light level: what is relevant is not the light at the spawner but the light at the location where the mob spawns, so putting a torch on the spawner is just a way to center the light, not inherently good — and is in fact inadequate to light up the full spawning range to level 8, though it happens to be sufficient for many natural dungeons. The actual requirement for safety is that the full spawning area (8×8 × 3 high box centered on the spawner's low-coordinate corner) is sufficiently lit (or does not have valid locations to spawn, e.g. is filled solid).

In your case, where you have two spawners right next to each other, there is no way to spawn just the skeletons except by lighting or filling up with blocks the entire spawn volume of the cave spider spawner, leaving you with just a thin slice of skeleton spawner volume (which will therefore have lower spawning rates).

Another possibility would be to construct a sorting system which separates the skeletons from the cave spiders, but I don't know of a particular design to suggest. Cave spiders are particularly difficult to handle because of their small size and ability to climb.

Well, Creepers can blow up stone and cobblestone, both of which have blast resistances of 30. Since a spawner has a lower blast resistance of 25, it can certainly get taken out by a nearby Creeper blast.

I suggest closing off side tunnels and keeping the area very well lit while you are nearby doing any mining or construction so that Creepers can't spawn. Then remove the lighting near the spawners when you are done (so they can start spawning again).