If we were to determine the user's preferred date format based on their browser's preferred language codes, how reliable would this be? What language tags/country codes would map to what?

Date formatting is essentially a feature of language, so this would be an appropriate use of the tags. en-us always formats as mm/dd/yyyy, while en-gb always formats as dd/mm/yyyy, for instance.

(Based on Calendar date and the list here)

January 15, 2001

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15 January 2001

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2001 January 15

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2001-01-15

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???