There is so much redstone-devices you can create, I can't name them all :).
You can create any sorts of devices. From simple light systems to mini-games ingame. You can create a game of hangman in minecraft, a piston dam, arrow gatling dispenser to all kinds of things. To see some complex example of redstone wiring, have a look at FVDisco and Sethbling's creations.
You have to mine redstone ore.
Redstone Blocks now exist in Minecraft 1.5. You can make them by combining nine redstone dust on the crafting table.
You get redstone dust and place it on the ground or a block. You can't put redstone wire on walls or roofs.
Yes.
Make a redstone circuit.
redstone torch
You mine it from redstone ore.
Redstone is the electricity of Minecraft. Using Redstone, one can make a infinte variety of electrical devices such as arrow traps and blowing up TNT.
Redstone acts like a wire you can use it to make doors open and to make minecart tracks and more
To make potions last longer, you add redstone to them.
You need an iron pickaxe to get redstone in Minecraft.
Its called a redstone lamp. It is crafted with a glowstone in the middle and four pieces of redstone around it.