Which of the sentences below is the most correct when asking for
specific location, and why?
Where in Australia do you live?
Where do you live in Australia?
Both sentences are grammatically correct. I would lean towards the first one and would phrase it like "whereabouts in Australia do you live?". The reason that I would choose the first option is because the focus of the sentence is "in Australia", meaning that you want to know the exact location within a specified country. The second option focuses on "where do you live", with the "in Australia" sounding almost like an after thought.
Here, is 'In Australia' an adverbial phrase as well as a prepositional
No, "in Australia" is a prepositional phrase. "In Australia" starts with a preposition and ends with noun, keep it simple :)
If so, is there a rule for where in the sentence it should go (or
where it should go in a sentence)? I read somewhere that adverbial
sentences can be at the front, in the middle or at the end of a
sentence. However, acccording to sources, changing the position of
adverbial phrases can alter the meaning/implication
Take a look at the full sentence. In the sentence "to live" is a verb, I live, she lives, they live. The preposition "in Australia" describes the verb, thus you are correct by saying that this is an adverbial phrase. Note also that a prepositional phrase can also modify an adverb and an adjective, also then acting as an adverbial phrase.
I would normally expect the verb to come first, for example
- "she really wanted to stay in Australia"
- "he lost his luggage in Australia"
both examples being prepositional phrases that describe a verb and I have put the verb first before the preposition, this is quite common.
However, the examples above also work the other way round, such as
- "It was in her birth country of Australia that she wished to remain"
- "they were informed that it was in Australia that the luggage was lost"
So as you see, the position alters the meaning by flipping the focus, is the focus "Australia"? or is the focus that she wants to stay there, or of the many countries visited, that was where the luggage was lost?
and 'In Australia, where do you live?' sounds to me that the person have homes
in multiple countries. Am I correct in thinking that?
Yes, that would be my interpretation also.