Good points. I see three specific problems with “And you are …?” when directed to a non-native English speaker, particularly an Asian:
• It’s only half of a sentence, and you’re asking the person to complete the sentence … in a language they don’t completely understand, and which uses a completely different syntax than their native language.
• In English, we shift the pitch of our voices upward at the end of a sentence (or in this case a half-sentence) to indicate a question. In Japanese (at least as I understand it from my failed attempt to teach myself the language from a book) and perhaps other Asian languages, a speaker shifts his voice pitch down at the end of a sentence to indicate a question. So the Asian listener doesn’t pick up on the inflection and immediately recognize the words as a question. He hears what sounds like a statement: “I’m Enola Straight and you are.” (On that note, I’d also strongly suggest using “My name is …” rather than “I’m …” or “I am …”)
• Most people, when learning a foreign language, are instructed in the “formal” usage. While (I’m told) most Japanese take English classes in school, the focus of those classes is on reading and writing English, not so much speaking it. So their instruction doesn’t include “figures of speech” to any significant degree. In “formal” written English, you don’t start a sentence with “And”. That would confuse a non-native speaker.