One Nation under God, upholding democracy and the principals of the Ten Commandments? -

Actually no, America was founded on the opposite, and was all the better for it.

Which country has a constitution which declares 'one nation under God', America or Iran?

Iran

Were the majority of the people on the Mayflower fleeing religious persecution?

No. (Most people who fled to America were fleeing persecution FROM religious people. By 1776 America was a secular as modern Europe, while Europe was as religious as current day America.)

Does American law contradict the Ten Commandments?

Yes, capitalism is based upon the idea that coveting things is not that bad after all.

Did the American Constitution mention God?

No

Is the American Constitution based upon purely democratic principles (i.e. majority rule)?

No, it specifically protects minorities from majority voted laws which persecute.

Is America a Christian Nation?