Question

He recorded his life there in his diary.
=> He recorded his life in Antarctica in his diary.

1. Which life did he record in his diary?
2. Which life of his did he record in his diary?
- He recorded his life in Antarctica in his diary.
[Which question is suitable for the answer?]

3. Where did he record his life in his diary?
- He recorded his life in his diary / in Antarctica. [3-1]
- He recorded his life in Antarctica in his diary. [3-2]

[If somebody asks this question, can we answer as in the above? In this case, is 'in Antarctica' an adverbial phrase? Can we use [3-2] as a suitable answer?]

Answer 1

In all these sentences, "in Antarctica" is an adjective modifying "life."

Since we all have only one life, I wouldn't use either 1 or 2. I'd ask, "What part of his life did he record in his diary?"

If you want "in Antarctica" to be used as an adverb, then here's how:
~ In Antarctica, he recorded his life in his diary.

Remember, as I've written before -- the adjective or adverb needs to be as close to what it's modifying as possible to be crystal clear.