I still recommend doing AKL-MEL on the OWE ticket and buying a Red-eDeal on QF for MEL-SYD, if you can rearrange the order in Oz. Not only will you save the US$50 but you will get to fly across the Tasman in D, rather than Y, thus getting many more status miles. You will get 1643 actual miles for the AKL-MEL trip and 2054 Q points. The SYD-MEL in D is only 440 miles and 550 Q points. Also, effective next year, QF will only give 50% credit for discount Y, so you would only get 822 miles and Q points for the AKL-MEL cheap ticket.

AY flies DXB-HEL on Mondays. Check one of those dates as they do show that they fly the route on 8 and 15 March.

You can book with any of the airlines although given your SIN origination, I'd go with CX. If you don't like the service there, use AA.