If you are just starting out, not really, you just have to do all the quests that give Under-city reputation. If you are 78-80 you can do the argent tournament quests that will get you exalted fairly quickly.
The Undercity is the capital city for the Undead. It is built under the ruins of Lorderan.
You find the Fire Launcher in World of Warcraft by going to Orgrimmar or Undercity. They all have them!
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The best way is to do the Argent Tournament dailies in Icecrown. This is a good way to get exalted with your factions cities too.
Yes you must be Exalted with the Nethwerwing faction found in Shadowmoon valley and have epic flying to attempt to start gaining rep.
No, I have not ventured into the undercity in the world of Magic: The Gathering.
You buy it from th wyrmest accord quartermaster but you must be exalted first
Yes there is. You do not need to be exalted with your home race to buy mounts from them at the appropriate experience levels. For example: if you are a human, you can get the human's mount at any reputation level, but Night Elves must be exalted.
Sylvanas is the leader of the Forsaken. She was once Lady Sylvanas Windrunner, a general for the high elf army, but was converted into a banshee by Arthas when the Scourge invaded Silvermoon. You can find her in the Undercity.
Varian Wrynn can be found at the throne room in the Keep of Stormwind. He also features at the quest for Battle of the Undercity, and is standing in the starting hall of Icecrown Citadel.
The Tauren racial mounts can be found at the mount vendor in Bloodhoof Village in Mulgore. You have to be exalted with the Tauren if you are not a Tauren.
You can purchase an item called "Nurtured Penguin Egg" that allows you to summon "Pengu".