From my experience it's somewhat luck of the draw when it comes to this. They often give you the option to stay onboard, but other times you all must disembark. I have only flown EK412/413 between DXB-SY-DXB, haven't been through to Auckland, so don't have first hand experience of this route.

Depending on how long you have you will definitely be able to use the SYD lounge - no probs.