Is it possible to book, for example, AKL-SYD-HNL with QF but actually begin the journey in SYD (that is, not board in AKL)? Similarly, HNL-SYD-AKL, disembark (permanently) in SYD? No checked luggage is involved.
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If you no-show any flight on your itinerary, most airlines will HX/Cancel every remaining sector and will refuse to check you in or board you on subsequent flights.
Cancelled flights aside, it would break the rules of the airfare which has a specified departure and origin.
With the second question pertaining to HNL-SYD-AKL, is AKL is your final destination, there's nothing to stop you from not utilising the SYD-AKL flight as there's no further sectors for the airline to cancel.