See 14th amendment and Art IV, Sec. 2
This is about immigration and does not alter the qualifications for president. If it did, it would have said so.
Yes, but the 14th in no way can redefine the original meaning of the phrase when it the Constitution was ratified, and of course Congress has no authority to arbitrarily assign a meaning either, even if the Supreme Court says they can. To “fix” this a simple amendment striking the language entirely is needed.
http://powderedwigsociety.com/eligibility-of-cruz-and-rubio/#
Pretty straightforward and easy to understand presentation about Cruz and Rubio’s eligibility to run for POTUS.
The link also explains why the 14th amendment does not apply.