Mexico has many races. 60 percent is Mestizo, 15 percent White, 15 Indian, and 10 percent Asian. I had friends from Mexico who are White. I have seen a lot of non-Spanish last names in Mexico and Latin American countries. I see lots of English, German, and Irish last names in those nations.
Correction, 5 percent Black and 5 percent Asian. Mexico's Blacks live in Costa Chica southeast of Acapulco. They face lots of racism in Mexico. The Asians are usually Koreans, Chinese, and Japanese.
Yes. The "Indians" also weren't one big happy family either --- there are many different groups of them. A Tarahumara has little in common with a Mayan and so on. Both would be lumped together under the umbrella word "hispanic" even though they have a different culture and language and often don't speak Spanish. Vicente Fox himself has an Irish last name and his mother came from Spain -- not really what most people consider a typical Mexican --- but then most people will call people in the USA with Spanish blood especially in areas of the SW "Mexicans" even if they never once stepped foot in Mexico and if their families never lived there.