I think you handled that well. Also that your concern about fake police was well founded. That she was a woman alleviates it some, but not altogether.
Regarding the language issue, it's hard to judge its appropriateness without knowing where the interaction took place—city, neighborhood, etc.. I don't expect you to reveal too much about where you live on a public forum, but it's something to think about.
I grew up in LA. While no one would take me for Latino, there are certainly parts of the city where Spanish would be the default language. Although the cop made an incorrect assumption, is it possible she was attempting to show respect by addressing you in Spanish? I mean it's a bit of the glass-half-empty scenario.