Is "middle narration" acceptable to native speakers?

(132) She asked him why did he not write out his thoughts. (middle narration)
She asked him, "Why don't you write out your thoughts?" (direct narration)
She asked him why he didn't write out his thoughts. (indirect narration)
Source: https://www.google.com.tw/books/edition/英語應用語言學研究入門_上/QzyRDwAAQBAJ?hl=en&gbpv=1&dq="middle+narration"&pg=PA176&printsec=frontcover

Is "middle narration" acceptable to native speakers?

Are you asking if the term "middle narration" is acceptable? I've never heard of it. Additionally, "She asked him why did he not write out his thoughts" is ungrammatical.

1. I wonder, "Will they finish on time?" (direct narration)
2. I wonder whether they will finish on time. (indirect narration)
3. I wonder will they finish on time. (middle narration)
4. Will they finish on time, I wonder? (middle narration)
Source: Source: Ting-Chi Tang, A Guide to Teaching Junior High School English, pp333-334.

Are #3 and #4 acceptable to native speakers?

I also had never heard of middle narration before.

The first one is what I would call a direct question, and I'm not sure why "I wonder" is in there.

You could put "What do you think?" either before or after the main question.

The second one is what you might call an indirect question. That is, you're asking a question without really asking a question.

For #3 you could say, "I wonder if they will finish on time."

For #4, you don't need "I wonder".

5. He asked me, would I go with him as far as Reading? (middle narration)
6. He asked me, "Will you go with me as far as Reading?" (direct narration)
7. He asked me whether I would go with him as far as Reading. (indirect narration)
Source: Ting-Chi Tang, An Introductory Study of English Applied Linguistics, p176.

#6 and #7 are grammatically correct. Is #5 also acceptable to native speakers?

No.