They share a common border.
No, the capital of Mexico is Mexico City. New Mexico is part of the United States.
Mexico lost half its territory, including New Mexico, at the Mexican-American War of 1846-1848.
Oregon. New Mexico was part of Mexico until 1848 and Idaho was part of Oregon until 1846.
partly, not really most of it was gained through the Mexican war and the remainder was "bought" through the Gadsden purchase for 10 million dollars