I also find this question confusing. This one came across me many times.
For me correct answer should be :
1. He asked the interviewer if he could please repeat the question.
I think you are preparing for SSC CGL or IBPS. Most of the books have given the answer "He requested the interviewer if he could repeat the question", as mentioned by you. But this is incorrect. We can't use "request" here.
- He requested the interviewer to repeat the question.
Original question is not an imperative one. So use of "to" is not correct here.
................................................................................
In Object general english by SP Bakshi, you can find a question with same structure.
1. She said to her friend,"could/would you please lend me some money?"
Answer : She requested her friend to lend her some money.
This answer is given in Book. But I doubt if it's correct.