1. If the natural born allegiance were only associated with the place of ones birth what would be the natural born citizenship of a baby born to US citizen parents on a ship sailing under the Liberian flag in international waters?
Under US law, the child would be a citizen. There has long been dispute about if the child would be a natural born citizen or not. I suspect the courts would rule yes, if asked.
2. If a baby was born in the USA to illegal aliens (Mexican citizens), what is the natural born citizen status of this child?
The courts have held that NBC applies to a child born of parents here in amity - with the acceptance of the US government. The child of an invading army, however, is not, since the parents are not here with permission of the US government.
It would be interesting to get a court ruling, but while I think the answer is no, I also think there is at least a 50:50 chance the court would rule yes.
And if they were Mexican tourists, here with permission, then the answer is undoubtedly yes.
3. If the same Mexican citizen parents had a baby born in Switzerland, would the baby be a natural born citizen of Switzerland?
Beats me. The Swiss have different terminology and laws. Our Constitution, as the courts have consistently held, is interpreted in light of the English common law that provided it the language of law. That is why Vattel is irrelevant to discussions of citizenship under the US Constitution. He is used as an authority when the citizenship involves vessels on the high seas, or on questions of foreign citizenship.
The change of US Immigration law (from 1790 version to the one adopted in 1795) indicates that early legislators did not equate citizenship at birth and NBC. The first law (1790) is the only one in the USA history using the phrase NBC (to describe the status of children of US citizens born abroad). The law was changed only five years later and such children were declared as citizens at birth.
If early legislators did not think that two phrases were synonymous - neither should we.
Hamilton suggested that the eligibility requirement for US presidency be citizenship at birth. We know that the adopted language explicitly mentions NBC. The moment we start arguing whether a person is a NBC, the debate is over. When it comes to the NBC definition there is no ambiguity, no debate is needed. Such a child can only have the citizenship (allegiance) at birth to one country. .
The WKA case ruling declares a child born to permanent resident parents a citizen at birth - not an NBC.