Short answer
Sentences 1, 2 and 6 use the preposition to because, in those examples, the verb been represents the verb GO. The verb GO often takes to-Complements. We (usually) say go to a place because a to-preposition phrase represents a destination or goal.
In the other sentences the verb been represents the verb BE. The verb BE often takes in-phrases. In-phrases most often represent a location, not a destination (in standard Englishes).
Full answer
The word been can be one of two verbs in English. It can be a past participle of GO or it can be a past participle of BE.
When we use GO in present perfect constructions, we use the participle gone to indicate just going, and the participle been to indicate going and coming back.
- Bob's gone to Paris.
- Bob's been to Paris.
Sentence (7) implies that Bob is still in Paris but sentence (8) implies that he is back again.
The verb GO normally, but by no means always, takes a to-preposition phrase as a Complement. Here the to-preposition phrase indicates a GOAL of the original journey.
The verb BE often takes in-preposition phrases. In such cases, the in-preposition phrase indicates a (usually stationary) LOCATION but does not necessarily invoke any idea of movement, goal or end-point.
Let's take two past simple sentences using the verbs GO and BE:
- My friend went to Sardinia.
- My friend was in Sardinia.
If we change these sentences so that we have present perfect verb forms we get:
- My friend has been to Sardinia.
- My friend has been in Sardinia.
The Original Poster's examples
- Has your dad ever been to Australia?
- Yes, he's been to Australia twice.
- He's been to Australia for Christmas.
The three examples above all illustrate the use of been as the past participle of the verb GO. The past simple of these sentences would be:
- Did your Dad ever go to Australia?
- Yes, he went to Australia twice.
- He went to Australia for Christmas.
Examples (1-3), like the past simple sentences above, use the preposition to to indicate the goal of the movement. These to-preposition phrases are selected specifically because of the verb GO here.
We can contrast these sentences with the other examples from the Original Post:
- Is he in Australia now?
- Yes, he's been away for about a week.
- Where has he been?
The past simple versions of these sentences would be:
- Was he in Australia (then)?
- Yes, he was away for about a week.
- Where was he?
We can see that these sentence all use the verb BE. They take a range of preposition phrase Complements, headed by the prepositions in, away and where respectively. These preposition phrases, as is common with the verb BE, all indicate a location as opposed to a goal.
Interestingly, the Original Poster's last two examples, (5) and (6) use different beens, arguably different verbs:
5: Where has he been?
6: He's been to Australia for Christmas.
The past simple version of this conversation would be:
- Where was he?
- He went to Australia for Christmas.
Notice that the speaker of (6) could have said:
The past simple version of this would be:
Hope this has been interesting!