What is the difference between a joule and a watt? What is a kilowatt in relation to a watt? Is there such thing as a milliwatt?

The difference between a joule and a watt is the difference between energy and power. Power is energy used in a certain amount of time. A joule is a unit of electrical energy equal to the work done when 1 amp passes through resistance of 1 ohm for 1 second. A watt is a unit of power equal to one joule per second.

As with all metric prefixes, kilo means 1000. So, a kilowatt is indeed 1000 watts. And yes, milliwatt is a valid unit of measurement, equal to 1/1000 of a watt.

Joule is a what per second ?

One kilowatt-hour means you are using energy at the rate of 1 kilowatt (1000 watts, or 1000 joules per second) for a period of 1 hour. An hour is 3,600 seconds. If you use 1000 joules each second for an hour, that's 3,600,000 joules. So 1 kilowatt-hour is equivalent to 3,600,000 joules. Do you see why your utility company prefers kilowatt-hours? Charging by the joule would be kind of like buying petrol for your car by the drop rather than by the gallon. Of course, they could just as easily call a kilowatt-hour 3.6 megajoules (3.6 mJ) or 3,600 kilojoules (3,600 kJ).