I agree and furthermore, according to some web searches I did, it seems much more common to say ‘a carteira’ than ‘sua carteira’ in this situation. And that in turn means that ‘the purse/wallet’ and ‘the handbag/purse’ should not be accepted here, because it instils wrong ideas about how Portuguese works into aspiring language learners like yours truly.
"Store" should be considered correct. Duolingo is deficient in its database of translations. I would say that in this sort of statement, to "store" is exactly the same as to "keep". Re topaz20's question, I'm not sure if "guardar" implies the action of putting -- we need a native speaker to answer that. In English to "store" could imply this action, although this latter sense doesn't take away from its equivalence with to "keep".
too subtle for my ears since the speech is crazy fast anyway. No diction apparently in Brazil. Having visited Portugal and listened to news casts, without knowing much of the language, I could understand more. It just reinforces my thoughts that I'm never visiting Brazil if they talk that fast. And if articles are regularly dropped/implied in written language, what's the point of including them at all in translations?
Does Duo represent spoken language accurately then? The dude's voice on Duo sounds like he's practicing to be an auctioneer. The woman's voice is slower and much easier to understand. Dropping sounds I understand happens, and yes very much in English too. Dropping words in speech that you expect listeners to pick up in their written responses is something completely different.
I can't speak for Duo, but agree that it's imperfect in many ways, e.g. clumsy translations, or good translations being rejected. You get what you pay for. The voices especially can be worse in some languages vs. others. I wouldn't use the voices as a guide to how the language is actually spoken (especially to the extent that you wouldn't visit a country based on Duo's bad approximation; but, if you're used to European Portuguese, getting used to Brazilian would definitely require some adjustment). Better listen to radio stations, podcasts etc.