Looking at this fare AMS-FRA-SIN-SYD, it’s possible to do SIN-SYD in QF First. Would baggage be checked all the way through even though LH and QF aren’t in the same alliance?

What then happens if I add a SYD-ZQN sector with QF on a different PNR? The Qantas website says that baggage can be checked through if it’s QF to QF on different PNRs, but I assume that doesn’t account for there being two Lufthansa segments before.

Assuming that I couldn’t check the bag all the way through from AMS to ZQN, can I opt to collect in SIN and recheck with QF all the way from there, to save the rigmarole of entering Australia in the morning peak?