Is Mexico Republican country

Answer 1

Yes. The country you know as Mexico has a "federal representative republic" style of government. In fact, Mexico is the nickname of the United Mexican States, as it is known officially.

Se related questions for further explanation.

Answer 2

If you mean whether New Mexico is a republican or "red state", the answer is no: it has been mostly a democrat state for three of the last four elections.

If you mean whether the country of Mexico is a republic, yes, it is a federal presidential representative republic, just like the United States.