There is Fact Sheet available from DoH which is the basis for some of the information provided here.

Do I have to register with the PHN to get my PIP QI payment?

Yes, registration is required by 15 October to receive the 31 October payment.
Registration is made via your PRODA account.

See section 6 or 7 of the fact sheet

Do I have to allow the PHN to extract data using their data extraction tools?

No you do not have to use the PHN provided extraction tools:

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