"If m = 2kg then I must multiply that by 2 and get 4 = 4*1 kg which is a square."

A kg is a unit of mass, a "square" is either an arithmetic term or a geometrical shape. They have nothing to do with one another.

"Then about 300,000 km/s * 300,000 km/s = square m/s. 9*10^16"

I'll be charitable and assume you did a typo, because that statement is meaningless.

"Then this would indicate to me that 3.6*10^17 square meters would be radiated in one second if 2 kilograms of mass would be converted to energy."

"Square meters" cannot be radiated at all. We are talking apples and oranges here.

What you are trying to do here is determine how much energy can be released if 2 kg of matter is completely converted to energy using the Einstein equation,

E=mc^2.

E = (2kg) (3x10^8 m/s)^2

E = 2kg (9x10^16) (m/s)^2

E = 1.8 x 10^17 (Kg m^2)/s^2

The unit (Kg m^2)/s^2 is the unit of energy, it is(in English) "a kilogram-meter squared per second squared", it is often abbreviated as the "Joule". One Joule is roughly the amount of kinetic energy in a one pound mass traveling at about 3 feet per second. Using the vis-viva equation of kinetic energy or E = 1/2 mv^2.

E = mc^2 is an absolutely ENORMOUS amount of energy, and we cannot generate this kind of power by any craft we now possess. Even a thermonuclear weapon utilizing hundreds of kilograms of fissionable and fusionable material only converts a few grams of that matter to energy. The thermonuclear reactions in the cores of stars only manage to convert a few percent of the mass involved into energy.

A radioactive nucleus converts a tiny amount of its mass to energy (less than a percent) when it decays, but most of the matter is left behind as plain old matter. Your notion that our use of nuclear weapons and reactors is equivalent to a complete conversion of thousands of tons of uranium/plutonium to energy is simply not true. As far as I know, there is no process in nature than can completely convert matter to energy. At most a few percent is converted. The bulk of the matter survives as stable daughter nuclei.

All the energy created by all our nuclear technology (plus all the energy subsequently released by the radioactive decay of all the products) is insignificant compared to the sunlight received by the earth in just one second. The earth receives from the sun about a thousand Joules of radiant energy PER SQUARE METER every second. That's about a kilowatt per square meter.

PS. A Watt is a unit of power, which is energy divided by time. A Watt is a Joule per second, or J/s. See how useful units are?