"I like a girl."
Translation:Мне нравится девушка.
The literal translation of мне нравится is "to me is pleasing" and thus we need to use dative case because we are receiving something. I know the English translation says "I," but you need to consider the cases and constructions used in Russian, and the difference between любить and нравится.
This is pretty strange in English. I feel like you need кое-какая (I'm hinting that I like someone, but I won't say whom) or какая-то (a certain girl, but I don't know her name). To me, this sentence has to have something implied. Even if this in response to "There's no way you are interested in anyone" [no, in fact I like a girl], I think the article "a" needs something in Russian to capture that.
Одна makes sense too. I'll never really know what sounds natural to a native speaker or not (but I'd imagine Мне нравится кое-какая/какая-нибудь девушка would be awkward), but this sentence just sounds strange in English, and I think you need something to convey the "a" in Russian. I get that Duo is trying to teach the нравиться construction, but I think they could come up with better simple sentences than this.