I haven't been to Australia since I was child and born in Hong Kong.

[output]

Is the following sentence correct and natural?

I haven't been to Australia since I was child and born in Hong Kong.

 

[Rover_KE]

It's not. It should be at least two sentences.

If you insist on putting three nuggets of information into one sentence, you need something like I was born in Hong Kong and was taken to Australia as a child, but haven't been back there since.

 

[output]

Thank you.
May I understand correctly?
My sentence is talking about I have never been to Australia but your sentence is talking I moved to Australia and never come back. Yes?

 

[Piscean]

No.

Both sentences inform us that you were in Australia as a child.

 

[tedmc]

Is the following sentence correct and natural?

I haven't been to Australia since I was child and born in Hong Kong.

What does going to Australia have to do with you being born and spending your childhood in Hong Kong?

 

[emsr2d2]

I haven't been to Australia since I was child

The part above is grammatical and makes sense. It's a perfectly good sentence on its own.

and born in Hong Kong.

This part does not make sense and it's what makes the original sentence ungrammatical and nonsensical.

 

[BobK]

I have never been to Australia

In that case your 'since' is misleading - I'd hesitate to say wrong, because it could be justified in a context like this:
"Ever since I was a child, although I was born in Hong Kong, I have never been to Australia."