Re: interpretation of one sentence
The only time I have ever actually read or heard this used, however, is in a novel or movie when one character is saying "you seem to know me/my name, but I don't know you/your name."
It wouldn't be used, from what I have seen, to mean "You know the capital of Nepal and I don't" or "You know what time the train from Liverpool arrives and I don't."
I've never heard this used in real life.
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.