"counter questions" is correct and usable in written English.
Example sentence: She countered his questions with some of her own.
Batwoman When first created by DC in 1956, Batwoman was intended as a love interest for Batman, to counter questions about his sexuality.
To counter questions about his stand on these issues, he pointed to the millions of dollars in support included in city budgets in recent years for gay-oriented groups like Lesbian and Gay Community Services Center, with whom he marched.
Don't ask counter questions or make any statements that would encourage conversation.
Ask counter questions wherever possible, e.g. If s/he asks: "where do you stay?", counter it with "what about you?" When they crack jokes simply smile.
Our rationale here is grounded on the counter question: What else could be more relevant to assess prediction rather than its correctness?
As a counter question one can ask whether it is justified from the perspective of Finnish taxpayers not to exploit the enormous commercial potential which Finnish biomedical research has produced during the past years?
He countered questions about his vitality with a vigorous performance at a debate on Monday, and floated through Election Day giddy on the energy of the young volunteers jumping up and down on street corners waving Mondale signs.
Mr. Guzman lashed out at defense lawyers during cross-examination with taunts and counter-questions.
He replies with a counter-question.
— without forgetting that the counter-question Mr. Dylan has posed is more challenging and, for a movie, more important: How does it feel?
(To which one counter-question is, Who does he think he is?) Philip Gourevitch writes in The Talk of the Town this week that unattractive aspects of his character were common conversation in Paris.
