That's a lot of questions! You need not give me the "brainliest," as I may only respond to a couple of those points for the sake of time here.
#2 in your list: In Lincoln's first inaugural address, he said: "Plainly, the central idea of secession is the essence of anarchy." In other words, if states could choose to secede from the union, then there was really no union and no government. (Anarchy is the absence of government.) Only if we abide by the constitutional checks we place on ourselves in a democratic republic are we exercising genuine government. Otherwise, we fall into chaos or some sort of dictatorial state. Lincoln felt that the whole concept of self-government was at stake, threatened by the South's desire to secede. Lincoln had to treat the secession of several states as an act of rebellion.
#5 in your list (closely related to #2): The states that had seceded already had caused the civil war, in Lincoln's estimation. The northern states had to respond to hold the union together. The southern states claimed to be afraid for their property, peace and safety with an administration like Lincoln's in charge. But Lincoln saw those fears as unfounded, that all states would continue to enjoy their constitutional privileges. But seceding from the union cut them off from all stability and security.
In the Cold War, the United States (USA) and the Union of Soviet Socialist Republics (USSR) were at odds with each other because of strongly different worldviews. The USA was committed to capitalism and democratic institutions of government, whereas the USSR was committed to communism and imposed authoritarian government. Initially, the USA had atomic weapons and the USSR did not. (The US would not share that technology with the Soviets, who had been their ally in World War II.) But once the Soviets developed their own atomic weaponry, this led to a massive arms race between the superpowers. The two nations kept escalating their weapons capabilities and stockpiles. It got to the point that if the two sides did plunge into war, they would face mutually assured destruction. John Foster Dulles, the Secretary of State under President Eisenhower, wanted a change from what had been the "containment policy" which the US had followed during the Truman Administration, as recommended then by American diplomat George F. Kennan. Dulles felt the containment approach put the United States in a weak position, because it only was reactive, trying to contain communist aggression when it occurred. Dulles sought to push America's policy in a more active direction; some have labeled his approach "brinkmanship." In an article in LIFE magazine in 1956, Dulles said, "The ability to get to the verge without getting into the war is the necessary art." He wasn't afraid to threaten massive retaliation against communist enemy countries as a way of intimidating them.
Eventually (after decades of the arms race and tensions) the US and USSR would pursue policies of detente, which included pledges to reduce their nuclear arsenals. The arms race and solving the arms race were constant issues affecting the Cold War.
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