You may have your difficulty set to Peaceful. Monsters will not spawn in Peaceful mode.
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There are no hostile mobs in Peaceful difficulty mode on Minecraft. Mobs such as creepers, skeletons, zombies, spiders and all other manner of hostile mobs do not spawn while Peaceful mode is active, though you will see (in dark places or at night) mobs attempting to spawn and immediately disappearing a millisecond after appearing. Mobs cannot attack you regardless unless another difficulty is triggered.
You can get a mob spawner in Minecraft by using any pickaxe (except wood) with Silk Touch 1 enchantment or by spawning it in (Dec:52).
Get two mobs of the same kind together in a pen and feed them wheat. Hearts come out and they start bouncing each other and then there's baby mobs. Note you can only do this with passive mobs so you can't go around making baby creepers lol. For hostile mobs make a room without any light in there so they can spawn, and every now and again go in there and kill them
My understanding is they can spawn no closer than 16 blocks from you, and I believe up to 125 away outside of that 16 in any direction, up, down, left, right, forward, and back.
Skeletons can make any agressive mob fight. I've seen skeletons and zombies, creepers, spiders, other skeletons, and even endermen fight. I've even seen two spider jockies fighting.