Yes. On many occasions.
See related questions.
Spain invaded Mexico.
Confederate Brigadier General Henry Hopkins Sibley invaded the New Mexico Territory.
Mexico IS the homeland. If you mean which country invaded and colonized Mexico, it was Spain.
The so-called "Aztlan War" is a racist myth. As for the rest of your question, Mexico has never invaded Texas. Texas was part of Mexico, and Mexico tried to prevent Texas from declaring independence. The effort failed, but it is false to say that Mexico ever invaded Texas.
France invaded Mexico and set up Maximilian I as the new ruler for the so-called Second Mexican Empire.
France invaded Mexico to challenge the Monroe Doctrine and establish a puppet satellite state. They placed Ferdinand Maximilian of Austria on the Mexican throne.
The starting point of such invasion was the city and port of Veracruz, on the Gulf of Mexico.
if mexico invaded america, and if the central powers were victorious, then Mexico would receive as payment the land that the usa stole by war in 1846 under President Polk.
Cortes
Maximilian I, and the invaders were the French.
Hernan Cortes
Hernan Cortes