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Star Trek VI: The Undiscovered Country (1991) More at IMDbPro »

US President Richard Nixon (in office from 1969 to 1974) was known for his firm anti-communist politics. When Communist states China and the Soviet Union broke up their alliance in the sixties, Nixon perceived this as a perfect opportunity to gain an advantage in the Cold War against the Soviets, by improving relations with China. The visit was controversial, because China was at that time considered to be an enemy state. Paradoxically, this made President Nixon the appropriate person to visit Communist China, because he was clearly an antagonist to their government. Had it been a more moderate politician, then this person could have been blamed for having too much sympathy for the Chinese, or not serving the United States' best interest in negotiations.

Spock alludes to this fact, because James T. Kirk is the most famous Klingon adversary in the Federation, so they know that he will not let the Klingons off the hook easily during negotiations. They can safely send him to eliminate all suspicions of fraternizing with an enemy. It is also another reference to the Cold War, of which there are many in this film.

Spock is jokingly attributing the phrase to his own Vulcan culture -- a running joke throughout the movie with different characters. For instance, Chancellor Gorkon claimed Shakespeare must be read in its "original Klingon," Chekov claims that Cinderella is a "Russian epic," and Spock also refers to Sherlock Holmes as an ancestor.

The network TV versions not included there are three main versions available. First of all there's the old Theatrical Version. Later on an Extended Version was created that features several new scenes, e.g. Federation President's office scene. A detailed comparison between both versions with pictures can be found here.

There's also a Special Edition that features a slightly changed cut. A detailed comparison with pictures can be found here.

Kirk was on a diplomatic mission, and a fight between the two ships could have sparked an inter-galactic war. Kirk probably felt that surrendering was the best option to keep the peace talks on track, while buying time to resolve the mystery.

(The question has been revised to please AMSATcorp's comments. Next time, please make use of the discussion page or contact me thru my username if you have any criticisms.)

In the year 2293 A.D.(6 years after the events in the previous movie)

Because the real Kirk called him an idiot. Kirk has a long and infamous reputation for standing up to authority figures, though he probably hasn't insulted many of them as openly as he would a brutish Klingon. The warden, probably knowing of Kirk's general demeanor throughout Federation history and his hatred for their race, instantly deduced that the Kirk to the left was the real one. Or he could have been informed by his superiors to review Kirk's history before he arrived or after when Kirk was still incarcerated. Also, Martia, being a shape shifter and likely a fact known to the Warden, didn't have shackles on as made clear by the overhead shot immediately after the vaporizing. The Warden was instructed to kill all witnesses, and set the conditions for Martia to assist in the charade under the false pretense of a full pardon. Shooting Martia first was the logical choice further assureing that the truth would never come to light.

Praxis' explosion is a direct reference to the explosion of the Chernobyl nuclear power facility located near the small city of Prypiat (north of Kiev) in the country of Ukraine, which was then a republic of the Soviet Union. during the Cold War. . On April 26, 1986, the power plant experienced a meltdown of nuclear material due to, like the Praxis explosion, "insufficient safety precautions". More can be read about the disaster here. Many Cold War historians believe that this event, combined with the failed Soviet/Afghanistan war were the final events that brought down Communism in Russia, much like the Klingon Empire & the peace accords that followed.