#2 Simple explanation: Appliances use electric motors. A motor converts electricity into motion. An engine uses a fuel source such as gasoline to do the same job.
Even simpler explanation: engines explode internally ( it's not really an explosion but this is a good way to remember it, it's really combustion ) Motors do not explode.
#1 'cord' is the best answer if you're in the US. But since that's not an option, I would use 'wire'
A 'lead' is a short piece of wire usually used in a temporary capacity. Also known as a 'jumper' or 'jumper wire'