My question is simple: to become President of the United States, must
you be born on US soil OR born an American citizen, whether it be the
US or Vietnam for example.

If both your parents are US citizens born and bread, but happen to be
travelling in Timbuktu when you are born, are you barred from running
for President?

If you have to be born on US soil, do foreign  US embassies and US
military bases qualify as US soil.

Moreover, if you are born on US soil to illegal immigrants, do you
qualify.

It would be nice to have a reference to an official government site
which explains the different requirements.