Why are there three branches in the U.S. government?

Prior to the American Revolution the 13 states were British Colonies. Great Britain was ruled by a monarch who held almost absolute power (the House of Commons and Lords had some power but mostly served the will of the monarch.) The Founders of the U.S. saw the abuses that come from having political power concentrated in few hands (or in one person such as an absolute monarch.) The Founders split the powers & functions of government (the power to make law, the power to enforce law, and the power to judge law) into three separate branches. These branches are the Legislative Branch (makes law), Executive Branch (enforce law), and the Judicial Branch (judges or interprets law.) This was done to spread power out over three equal branches that would serve as a check on the other branches and to balance power among each other. The Founders did this to disperse political power in order to avoid the abuses they saw in the British Monarchy.

Was the U.S. Civil War fought over the right to keep slavery or was it fought for the right of the states to govern themselves, free from federal interference?

To the average solider in the Confederate armies it was a war for state rights; to be free from federal intervention. These soldiers came from the poorer white population of the South and truly believed they were fighting to defend their home. However, for the ruling elites and Southern Aristocracy, it was fought to defend the right keep slavery legal. The ruling class were able to make incredible fortunes by using the cheap labor of slaves. For them, the election of Pres. Lincoln represented a direct threat to the institution of slavery. Thus, ultimately, the Civil War was fought for the right to keep slaves and to keep slavery legal. Many of the articles of succession from the Confederate States explicitly states that the reason for leaving the Union was in order to protect the institution of slavery.

When the European explorers first met the citizens of "The New World" was it for contact or conquest reasons?

The European explorers first set out to find new trade routes to the East. However, in finding the Americas they discovered a land rich in natural resources and people. They quickly used the native peoples in order to exploit the new land for its resources and riches. Thus, the first encounter can be said to be one of conquest.