When you use this size wire do you put a .5 amp fuse on it to protect it. A friend has a lot of lights with fine wire like this.
No. Unless you intend to run a higher than usual current for this size wire. An LED connected to this wire is perfectly safe. The LED will require only 20 milliamps of current max. As GunRunnerJohn pointed out somewhere else, the size of wire required for this small amount of current is not visible to the naked eye. A fuse is not necessary just because the wire is small.