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No. Businesses at IAH (or in the United States in general, with the exception of the occasional business near the border) will not typically accept pesos. You'll need US dollars or a credit/debit card.
There are currency exchange locations at IAH. There are also ATMs available.
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No (buy food); yes (exchange them first).
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While you can exchange MXN into USD at almost any airport, you can get a much better exchange rate in Mexico. The best cash exchange rates are in Mexico City airport Terminal 1, where you can often find a spread as low as 1%.