No.
No. The lounge is in the Departures area so you can't go backwards to immigration in Arrivals.
No.
I have done this before, in BNE, was interlining from QF to Air Nuigini (hand luggage only) and went through the international transfer security and then found that the transfer desk airside was unstaffed so only way to get my BP was to go to checkin, and was able to go back through passport control. I had to talk to one of the agents but it wasn't a huge deal. Was a bit weird walking back through the Duty Free the wrong way!
Any reason why this would not work in SYD?