Mexican's don't use hispanic to refer to ourselves. Anyone born here would be mexican or if you became a citizen you would be also. Just like anyone that becomes citizens of the usa are american's. White people, "sons of europeans", are criollo's. You would be caucasian, but your wife would be criollo and your kids would be criollo as someone of european ethnicity born in mexico. Nobody would call them "hispanic" here, latino would be used. Mixed race people are mestizo's and indidgenous are, well indigeno. These 3 are 90 something percent of the races, there are negro's, etc.
I wouldn't expect you to. Hell, I barely even use the word myself when talking to or about someone directly. It'd be like me saying I'm a North American caucasian. Technically, it's correct, but I'd be using a demographic term to refer to myself, and it'd be all kinds of weird and awkward.
...I would get looks.
Like if I'm talking about Bill, he'd be Bill the Mexican, or Peruvian, or Puerto Rican. Nor would I use it when talking about Mexicans, or Peruvians, or Puerto Ricans specifically. Like I wouldn't say hispanics make great food. I'd say Mexicans make great food. But if I were talking about Mexicans, and Peruvians, and Puerto Ricans as a single entity, then I'd refer to that group as hispanic.
Most of the time, the word only comes up in politics or paperwork. It's not specific at all, just...like I said...an umbrella term.