Ted Cruz is not eligible. His dad is not a hero. His mom was a Canadian citizen when Ted was born. more or less ~ details are all on the post.
The only point you mentioned that has any bearing on the issue is the status of Cruz's mother... and I don't believe that allegation anyway.
So in other words, that entire wall of text was a complete waste of my time.
Generally if a point cannot be summarized quickly, it is either invalid, or unworthy of consideration.