The Lich King's weapon is called Frostmourne.
The Lich King's sword is called Frostmourne.
The commoner's sword could be considered a short sword, yes. It is a main hand sword, so it is intended to be used with one hand, and short swords are one handed.
No the white sword is actually called The L1 Sword and the Master Sword is the L3 Sword. The L2 Sword is the Noble sword, and The L1 Sword is called the Wooden Sword.
Cloud's sword is called the Buster Sword.
The sword was called Anaklusmos
Currently, the swords that you get from battered hilt quests are the best in the game.
No, Frostmourne is not a player equipable weapon. It is Arthas' sword. No one else can use it.
Sword handles are called hilts. See the link.
Gandalf's sword is called Glamdring, or "Foe Hammer."
The vorpal sword
Cortes Sword
In a sheath,that is what the sword case is called
The sword was called Anaklusmos