How can he be impeached as prescribed in the Constitution if he is not inside the United States?
You claim the Constitution does not extend past the borders.
There are no restrictions on the power of impeachment. The House can impeach any federal officer or judge whenever it sees fit. No judicial review.
The Senate can then impeach and remove from office any officer or judge that it sees fit, as long as it can pull together a 2/3 majority.
The Constitution in full does not apply outside the United States. This does not mean that none of it or the laws authorized by it apply. Obviously they do. Equally obviously, not all do, or why do we bother to maintain a lockup in Gitmo? It's because the full panoply of constitutional rights aren't in effect there.
All I initially said was that customs searches do not and never have required warrants under 4A.