"This is true for all chemical reactions, but is it true for nuclear reactions?"

No, and that's why they specified chemical reactions.

"In a nuclear reaction mass (which is potential for energy) is converted into kinetic form of energy."

This is correct.

"Since energy can not be destroyed, and in this kind of reaction the energy does not convert back into mass, then it must give a permanent increase of (kinetic) energy to the surroundings."

Ok, I'll accept that- if you also accept that in terms tonnage of mass converted the Sun does more in a second than human have yet to do and probably will do in the next 100 years:

"The Sun's energy output (3.86e33 ergs/second or 386 billion billion megawatts) is produced by nuclear fusion reactions. Each second about 700,000,000 tons of hydrogen are converted to about 695,000,000 tons of helium and 5,000,000 tons (=3.86e33 ergs) of energy in the form of gamma rays."
http://www.nineplanets.org/sol.html

"Sufficient accumulation of kinetic energy in the atmospheric molecules will cause disruptions in the climate of the planet."

Kinetic Energy does not accumulate in atmospheric molecules or atmosphere. Or I suppose, I could say that Kinetic Energy per it's definition doesn't accumulate anywhere [unless one discussing such things in large scales [lightyears distance or going thru such things as the Sun] .

Though I suppose what you really mean to say is that heat [potential energy] is trapped in atmosphere which again seems wrong if you are suggesting that this heat remains for any amount of time [such as a days or months rather than time periods on order of seconds or nanoseconds]. As for this energy causing "disruptions in the climate of the planet" this too vague for me to understand or even guess as what you are referring to.

"Since neither one of us knows the exact quantities of energy or the effects that are involved in this nuclear experiment, we can only speculate about the outcome."

Hmm.
First the earth has always had radioactive material. For example granite is known to be fairly radioactive. There is a lot of Granite on Earth. In terms of radioactive fuel there is a lot of that on Earth also. Radon seeps from the ground- google search: radon.

Now usually when there any discussion of the ore to mine nuclear fuel one has to have a certain degree of concentration of this stuff to be consider a ore:
Ore:
Definition: An ore is a material that contains a metal in such quantities that it can be mined and worked commercially to extract that metal. The metal is usually contained in chemical combination with some other element in addition to various impurities.
http://metals.about.com/library/bldef-Ore.htm

So, so instance there is millions of oz of gold in the ocean, but wouldn't normally call that gold "deposit" an ore- you can't mine it economically.

Uranium:
Estimated Crustal Abundance: 2.7 milligrams per kilogram
Estimated Oceanic Abundance: 3.2×10-3 milligrams per liter
http://education.jlab.org/itselemental/ele092.html

1000 milligrams equals a gram, 1000 grams equal kilogram so, on average per million kg of earth surface there is 2.7 kilogram of Uranium.
If you live in house which has a lot size of say 20 meters [about 60'] by 30 meters that is an area of 600 sq meters if the density of this ground is around 2, the first meter in depth is 1200 tonnes or 1.2 million kgs. So there will be around about 2 kgs of Uranium in first 3' depth in your yard.
The amount radiation from the decay of Uranium depends upon it's half-life:

"There are three different isotopes of uranium. They are:

uranium-234: half life = 244 thousand years, 0.0055% of all uranium.
uranium-235: half life = 704 million years, 0.72% of all uranium.
uranium-238: half life = 4.5 billion years, 99.28% of all uranium. "
http://volcano.und.edu/vwdocs/frequent_questions/grp13/question1420.html

Now, let's leave your yard and go to the broader world.
In a sq kilometer to say to depth of 10 meters and again at say, density of 2. That's 20,000,000 tonnes of earth and per 1000 tonne one has 2.7 kilograms of Uranium, so that's 54,000 kgs [54 tonnes] of Uranium.

"Earth — Surface Area: 510,065,600 km2"
from Wiki

So times 510,065,600 by 54 to get how many tonnes there is of Uranium in first 10 meters of Earth surface.

So, you have radioactive material on Earth since Earth was formed, but in addition radioactive material is being added daily and hourly:
TRITIUM:
"Cosmic rays interact with nitrogen (14N) or with deuterium (2H) and form tritium and carbon (12C). These are primarily interactions that happen in the upper atmosphere and the tritium falls to earth as rain. The unit curie is a measure of an amount of radioactivity. A curie (Ci) is the amount of a radioactive substance that has 3.7 x 1010 decays per second. The world wide production of tritium from natural sources is 4 x 106 curies per year with a steady state inventory of about 70 x 106 curies."

I wanted to find quantity of Trillion in tonnes produced, but anyways in my search I found this web page which give much better explanation of naturally occuring radiation:

"Shown in the table above, 82% of the total average annual effective dose is from natural sources of radiation, and of that, most is from radon. Of the other 18%, the majority is from medical diagnosis and treatments, with <1% from nuclear power and fallout"
http://www.physics.isu.edu/radinf/natural.htm

Go to that web page and read the entire thing.