how the ideas of three enlightenment philosophers influenced the creation of American government?

Answer 1

Thomas Hobbes who wrote THE LEVIATHAN in 1660 is one.
He wrote that the basis of power was the people - - that the consent of the people was necessary. But much more influential for America was John Locke who wrote (~1690) that all people have natural rights to life, liberty, and the fruit of their labors. Locke also wrote that government is an instrument of the people's will, and the people have the right to rebel if the government proves to be tyrannical or defective. The third was the Frenchman Montesquieu who wrote that liberty is best secured by a separation of powers - hence the executive, legislative, and judicial branches of our government in the USA.