Per USCode Title 8 Section 1401, Sen Cruz is a US citizen at birth and has never needed to be naturalized. He is a natural born citizen.
No, you are not correct. The act you refer to is a Naturalization Act. If Cruz’s Mom or later Cruz himself provided documentation to the State Department that his circumstances fulfilled the requirements of the statute he would be eligable to be a Naturalized citizen, never a natural born citizen.
That's naturalization law.
Statutes cannot supersede original intent. The framers didn't want any British Loyalists from Canada to be president.