"1) Who are you talking about ?" is correct. "2) Do you talk about whom?" is wrong. Wrong word order, and I am not sure about using "whom" here. "Whom are you talking about?" sounds more correct, but not quite.

The word "whom" doesn't make sense at the end of the sentence. It would be "Whom do you talk about?" Other than that, yes the sentences are similar. "Whom" is just a variant of the word "who."

I agree with Jacob, though I would add that 'whom' is very rarely used today. It is used sometimes in formal written language, but it isn't used much in spoken English as it is seen as quite formal and old-fashioned. It can also be used a bit differently from 'who', for example in the sentence 'whom/who do you talk about' either is fine, though 'who' is less formal, but you could also say 'of whom do you talk' and in this case you couldn't use 'who'.