3) in an attempt to find a solution to the growing slavery issue in the united states, the missouri compromise added missouri as a slave state. which state was added to the union designated as the "free" state?

Slavery had come to America in 1619. It existed through the American Revolution, even after Thomas Jefferson penned his famous lines in the Declaration of Independence, "All men are created equal. They are endowed by their creator with certain unalienable rights. That among these are life, liberty, and the pursuit of happiness." Obviously, slaves were not part of this equation. When it came time to write the Constitution, the word "slavery" was never used. Instead, the framers chose to use the term "other people." These other people were counted as 3/5 of a person for the purposes of representation in Congress according to the 3/5 Compromise. This compromise kept slavery in the United States intact. The founders also decided not to do anything about the issue of slavery for twenty years. Someone else would have to deal with it.
In 1820 with the admission of Missouri to the Union, the issue of slavery came up again. There was already a great deal of tension between the North and the South. The South was highly agricultural. It wanted to keep slavery as a way of life on their plantations. The North, which was far more industrial, saw this "peculiar institution" as unnecessary and increasingly morally wrong. One way the government tried to limit the tension was by keeping the number of slave and free states equal. So, in 1820, when Missouri met the requirements for statehood and applied for admission to the Union as a slave state, there was a problem. The balance of free and slave states would be destroyed.