That is not 100% true. Constitutional rights only apply to US citizens regardless of where in the world they are. The constitution does not grant any rights to anyone who is not a US citizen.
Absolute twaddle. There is no such thing as 'Constitutional Rights', as the rights enumerated in the BoR predate the Constitution. This makes them superior to any governmental division or jurisdiction. As explained in the DoI, they are inalienable, and exist as granted by the creator.