Cheap production of goods
The history of "the wave" is an object of some controversy, but it appears to have started in Canada in 1980, gained momentum in the United States, and then became a global phenomenon at th 1986 World Cup in Mexico. See the Related Question for more details.
Mexico fell to Spanish conquistadors and became a Spanish overseas colony for 300 years,
In 1824 Mexico became a republic.
yes
After the conquest, Mexico became known as Mexico.
Santa Fe became the capital of New Mexico in 1610. It became the capital long before New Mexico became a state in 1912.
Mexico became a republic.
It was a colony of Spain.
Texas split up from Mexico and became an independent republic. This conflict is known as the Texas Revolution or the Texas war of independence. See related questions.
Mexico became independent from Spain.
As far as I know, no president were born/lived in New Mexico.
Mexico-Tenochtitlan.