"in response to questions" is a perfectly correct and usable phrase in written English.
For example, "The CEO gave a lengthy speech in response to questions from the shareholders."
"In response to questions. . .
Soloway wrote in response to questions.
He nodded a couple of times in response to questions.
"The work isn't mere artwork," he wrote in an e-mail message in response to questions.
The figures were released in response to questions by Louise Haigh, Labour MP for Sheffield Heeley.
Yesterday you could raise your eyebrows and close your eyes in response to questions.
But it also insists that it be taught in response to questions.
In response to questions about efforts to obtain additional counterterrorism resources, D.C. I
Mr. Paulson said in response to questions that he shared the senators' exasperation.
Mrs. Whitman's comment came in response to questions by Senator Fred Thompson, Republican of Tennessee.
The coach was saying these things in response to questions about possibly changing his lineup.
