For the person who answers, respondent or correspondent are reasonable. (Some of the previous questions mentioned in comments also suggest answerer and interviewee.)
For the enquirer/asker/questioner/interrogator/interviewer, my preference is interlocutor (“A person who takes part in dialogue or conversation” or “man in the middle of the line in a minstrel show who questions the end men and acts as leader”).
Edit: As noted in a comment, and as is quite obvious from first sense in the definition quoted above, interlocutor applies to all persons engaged in a conversation. In following, let first sense denote the first sense mentioned above, ie conversation participant; let second sense denote the second sense mentioned above, ie, minstrel leader; and let other senses refer to less-relevant third or fourth senses like “An interlocutory judgement or sentence” or “Someone who takes part in talks as a representative of another person or organization”.
Regarding the second sense: Merriam-Webster.com includes first and second senses in much the same words as Wiktionary. Wordnik.com has both senses, in slightly different words. Memidex.com shows the following dictionaries (or things resembling dictionaries) as having at least senses one and two: Collins Dictionary, Wiktionary, Merriam-Webster, New World Dictionary, American Heritage Dictionary, Encarta Dictionary. In its quotes of the following dictionaries, Memidex shows at least sense one, with sense two not shown: Oxford Dictionary, Macmillan British Dictionary, Cambridge Dictionary.
These lineups suggest that sense two (minstrel leader) of interlocutor is not found in British dictionaries and is commonly found in American dictionaries.