"his questioning" is correct and usable in written English.
You can use it when you are referring to someone's questions. For example, "The judge was very thorough in his questioning of the witness."
Mr. Benedict continued his questioning.
5.27pm GMT Nigel Mills resumes his questioning.
Several car enthusiasts said Mr. Cuomo proved his auto-buff chops through his questioning.
His questioning mind withers under the pleasures of having nice words bound in nice covers.
He demanded that Mr. Gingrich pull an ad that contained an old quote of his questioning Mr. Romney's honesty.
To squeeze answers out of bureaucrats, he has had to hone his questioning techniques.
"He would know his subject so well that his questioning often sounded like an interrogation".
"I've learned something important," he said, after he declared an end to his questioning.
Altair's story is inconsequential, involving his questioning whether he is truly killing for the greater good.
I was wiser for his questioning.
I was angry about his questioning.
