Maybe your game level is on peaceful or you put torches around it.
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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).
You cant find a giant mob in vannilla minecraft but you can sumon him using a command or a spawner.
It is not possible to actually make a mob spawner in any version of Minecraft. Mob spawners are only obtainable via in-game commands or if you use a mod of some sort.
If you are looking for a way to pick them up, well, you can't pick mob spawners up. You can only destroy them with a pick but it can give you a lot of exp.
A ghast is a huge ghost like mob in Minecraft that lives only in the Nether, unless hacked or spawned with a spawner egg in creative mode. They are aggressive, shoot fireballs that explode on contact, and make a creepy crying and moaning noise. They do fly, and are personally annoying.