Everything you have stated is utter nonsense. Ted Cruz is not eligible. He was born on foreign soil outside the jurisdiction of the United States. A dual citizen is not a natural born Citizen.
As for dual citizenship, 3 of our first 4 Presidents were dual citizens, while serving as President. Nobody cared.
As for the other:
"It is not necessary that a man should be born in this country, to be 'a natural born citizen.' It is only requisite that he should be a citizen by birth, and that is the case with all the children of citizens who have ever resided in this country, though born in a foreign country."
- James Bayard, A Brief Exposition of the Constitution of the United States (1833)
The above quote was part of Bayard's discussion of qualifications to be President and Presidential eligibility.
Bayard's exposition of the Constitution was read and approved by the Great Chief Justice of the Supreme Court John Marshall, by the legendary Supreme Court Justice Joseph Story, and by the famous Chancellor James Kent, as well as other legal experts of the early United States.
Not one single person ever said he was wrong about his understanding of what "natural born citizen" meant.