What are the limitations of these two primary sources: Premier Nikita Khrushchev's report to the Twentieth Party Congress (February 1956) and President D. Eisenhower's special message to the congress on the situation in the Middle East (January 1957)? Please be as specific as possible.

The most significant limitation is the audience to which Khrushchev directed his speech. It is essential to recall that, in 1956, Russia was a closed society. What information the government of the United States knew about Russian society and government came from reports from defectors, spy missions launched by the United States, or a scattering of reports provided by other governments. Intelligence gathering is never easy, and portions of the intelligence gathered on Russia was suspect. Verifying the sincerity of Khrushchev's address—in light of the absence of a free press and in the historical context of what had occurred prior to his promotion to the leader of Russia—was based on as much conjecture as fact.
Khrushchev's speech to the Twentieth Party Congress denounced the cult of personality, a direct reference to the policies of Stalin. He proposed a return to the nostalgic era of Lenin where Marxism was a uniting force and not used as a divisional wedge between the governing bodies and the people. As a demonstration of his commitment, within a few months, thousands of political prisoners were released, and the United States interpreted the moves of the new leader to be more friendly towards democratic countries.
Khrushchev was not renouncing Marxist-Stalin doctrine but was rather reaffirming a commitment to the communist ideal of not elevating one person above others. The speech was an attempt to circumvent hard-liners (who wanted to double down on the discarded policies of Stalin) and to the people of Russia who had suffered under Stalin from political persecution and economic failure.
Like all political speeches, words here were carefully selected to reach out to different audiences, and Khrushchev wanted to present to the world a different Russia under his leadership, contrary to Stalin's Russia. Khrushchev said in the speech:

And the fact that we present in all their ramifications the basic problems of overcoming the cult of the individual which is alien to Marxism-Leninism, as well as the problem of liquidating its burdensome consequences, is evidence of the great moral and political strength of our Party.

He ended the speech by saying, "We are absolutely certain that our Party . . . will lead the Soviet people along the Leninist path to new successes, to new victories."
Eisenhower's message to Congress on the situation in the Middle East was a comparatively different speech in tone and audience than that of Khrushchev. Eisenhower was specific in laying the case for American intervention and increased presence in the Middle East to counter Russian influence.
Eisenhower intended to provide historical context to Congress concerning the history of Russia and the nation's goal to spread Marxist-Communism to the developing countries in the Middle East. Eisenhower said:

The reason for Russia's interest in the Middle East is solely that of power politics. Considering her announced purpose of Communizing the world, it is easy to understand her hope of dominating the Middle East.

Again, Eisenhower's audience was on a global scale; he hoped to warn (and perhaps appeal to) the Russian government that the United States was ready to support and defend countries in the Middle East that sought to form democratic governments.
The message was delivered to a skeptical Congress, whose members were mostly unfamiliar with American interests in the Middle East, and was delivered to reassure European countries of America's commitment to democracy. Eisenhower ended his speech with:

The occasion has come for us to manifest again our national unity in support of freedom and to show our deep respect for the rights and independence of every nation—however great, however small. We seek not violence, but peace. To this purpose, we must now devote our energies, our determination, ourselves.

In both speeches, the primary limitation of the speeches was that the targeted audiences were skeptical of the intent of the addresses. Both were addressing a world audience while simultaneously assuring their governing bodies that they would not be embarking on a dangerous path (one that could possibly lead to war without consensus).
However, both men wanted to establish a doctrinal principle from which to guide foreign policy and present to a world audience. Interpretation by different national interests would have been a limiting factor as well, as both men wanted to present a united domestic front, warn potential enemies, and strengthen ties with allied nations.
https://teachingamericanhistory.org/library/document/special-message-to-the-congress-on-the-situation-in-the-middle-east/

https://www.marxists.org/archive/khrushchev/1956/02/24.htm