For SIN check-in, QF/BA currently takes up rows 5 and 6 in T1, so if they indeed want to go for a split, I would imagine it's going to be a very simple arrangement of you take this row, I take the other. Interesting enough, 3K is next door at rows 7/8, while EK is not too far away at row 2.

And, looking at current flights, taking out QF's late night departure to LHR and FRA, BA only having 3 flights per day (1 to SYD, 2 to LHR), and EK's middle of the night departures (12 - 2am), they can all in theory share 1 check-in area.

With the lounges, I can't see why QF would want to us BA's lounges in T3 when it would make more sense to send pax to EK's one instead. But that remains to be seen.