The Americans were able to win the war for independence for a number of reasons. First, the British found it difficult to destroy the American armies in the field and simultaneously occupy American cities. Second, they grossly overestimated the extent of loyalist support (or at least loyalist military support), particularly in the South. Third, the war was deeply unpopular at home from the outside, and the Americans always had sympathizers in Parliament who placed significant pressure on a series of ministers to win the war. Fourth, British generals, through incompetence, indecisiveness, and lack of strategic vision, often failed to press their advantages, most notably in the New York campaign of 1776, when Washington's entire army was there for the taking. Fifth, Washington's leadership should not be downplayed. As commander of the Continental Army, he managed to hold the force together, keeping it viable and battle-ready as he led the British through what he called a "war of posts." Basically, although he made many mistakes and never really won a major decisive victory, Washington avoided defeat, making the conflict far longer, messier, and more expensive than the British were willing to bear. Finally, French aid, including French military assistance, proved decisive after 1778, and it is very unlikely the Americans would have been able to achieve independence outright without it.
They felt threatened because Socrates taught that people should be independent and question everything, including their government. They claimed that his was corrupting the youth and put him on trial because they felt that he would turn the people against the government.
Well no one city state won, the Peloponnesian League did, but it was led by Sparta, so that would be the best bet. As for the event most responsible for the victory, Sparta gained the support of the Persian empire, which allowed Sparta to raise a large fleet to challenge Athens.
