What way has democracy in Greece influenced democracy in American government?

Answer 1

The most visible influence is that US democratic institutions often like to dwell in buildings that are strongly reminiscent of Greek temples. That is because Greece traditionally is hailed as "the birthplace of democracy".

Truth be told, that 'birthplace'-story was an invention of British poet Alfred, Lord Tennyson, who loved everything Greek and who made up the slogan to drum up support for Greece when it tried to become independent from the Ottoman Empire in the 19th century.

In reality, most if not all of the Greek city-States were Olicharchies throughout their history. Which means that they were run by those cities' powerful families. The US' democratic institutions and beliefs are all the product of 18th century Enlightenment thinking and of Enlightenment philosopher Montesquieux.