Nice post-apocolyptic story. However, I wish to direct you attention to a grave mathematical error:

promises, the U.S. had developed a nuclear warhead with enough power 

to screw up the functions of nature for over a year in a radius of 
400,000 kilometers from the main target. The target had been Beijing, <<

A radius of 400,000km means a diameter of 800,000km covering an area of 502 BILLION km sq! Very impressive since the Earth's diameter is only 12,756km and total surface area is 511,185,932km sq. This mean the bomb's explosion will cover the planet over 982 times! 
Despite the insanity of developing more powerful nukes, I doubt anyone would be crazy enough to make a bomb that WOULD destroy themselves with the first detenation.