An originalist won't rule that he's inelgible since Cruz was born a citizen.
As an attorney, I'll put $100 out there that the judges are going to leave this in the hand of the voters. Judges don't want to make political decisions for voters when it comes to elected officials. (Another story when it's about social issues)
Scalia has already shown on two instances that he leans toward the requirement of Jus Soli for an NBC
Justice Thomas has said they are evading the Puerto Rico issue.
And yes, you are likely right. The Court isn’t going to touch this
Yes they will, if they understand the simple fact that being born a citizen via law (when, for most of the 19th century, children born overseas were not considered citizens) passed by congress is, by definition, "naturalization," and thus not the same thing as the founder's concept of natural born citizen.
I'll put $100 out there that the judges are going to leave this in the hand of the voters.
You might get your wish anyway since Cruz won't win the nomination. But if he did win, yes, he will be sued and they will take it to court.