So you do not understand what a democracy is and how it works.
Balance of the three branches of government and the rule of law and protection of minorities are the complementary requirements to the majority vote, to qualify for a democracy.
In the simplest sense of the word, none of that is needed. Athens had such a democracy, where a majority of people made a decision so. You are putting more stipulations on the word than are strictly necessary, hence why I said the democracy examples you gave would not be great places to live in.
That would exclude every parliamentary democracy in Europe, so no.
Also, the word 'democracy' does not appear in either the US Constitution or the Declaration of Independence, so it's weird to make the argument you are making. The Founding Fathers never envisioned a party system to begin with. Women and obviously slaves could not vote. The US has only been getting more democratic over time. Your argument looks a bit like historical revisionism to me.
The earliest "democracy" (demokratia) dates back to the Greeks (and for free men, anyway), and Aristotle's Politica will tell you a bit about it.