I'm by no means an expert but I see it's been eight hours since you posted and no takers so I'll have a shot at some of your questions.
SYD-LAX-SFO-JFK-LHR-MAD//BCN-CDG//TRN-FCO-HKG-SYD-MEL-SYD
I plugged your routing into
Mileage Monkey and it gave a couple of errors. The first was there is apparently no oneworld service BCN-CDG. There is - sort of. JAL have a codeshare with Air France but only oneworld carriers may be used on the oneworld Explorer product. (This includes codeshare so, for example, a QF codeshare on AA is permissable but not a QF codeshare on SA.)
Second, MM also says no oneworld service exists TRN-FCO. A quick check of the oneworld timetable using a few random dates seems to suggest this is indeed correct.
Is LONE4 the best product for the below itinerary?
The above routing issues would suggest a LONE4 isn't the best option. a oneworld Global Explorer may work as, to my knowledge, codeshares on non-oneworld airlines are permisslabe. However, I'm not familiar with their rules so can't help there.
Is it still beneficial to book through the AA RTW desk?
I have booked a oneworld Explorer (twice now) using AA ex-South Africa with significant savings. However, I'm not up with doing it ex-Australia. That said, there are a number of posts on AFF with advice on such so a search should give some good assistance.
Am I still able to do SYD-MEL-SYD on return?
I'm fairly confident in saying that no, this isn't permitted. Rule 4(b) of the oneworld Explorer states "Travel may not be via the point of origin". Not withstanding the above issues, one way to correct this would be to either originate in MEL (which means no A380 to LAX) or (ii) finish HKG-MEL-BNE-SYD, for example.
Can I upgrade to business class on QAN legs, SYD-LAX for example...?
Yes, L class fares are upgradeable. However, two points to note. First, only QF flight numbers on QF metal are upgradeable. So, for example, QF11 SYD-LAX, operated by QF, is upgradeable but QF3243 LAX-SFO isn't upgradeable as it is operated by AA.
Second, if ticketing through AA, it is likely they will insist that the transcontinental sector is on an AA flight number. In your example, this would likely mean booking either AA7365 (which is QF107) or AA7363 (which is QF11) on the SYD-LAX leg. If you do come across this issue, don't stress.
From my point of view there are two options. The first option is to simply book the AA codeshare flight and then, once ticketed, phone AA back and change to either QF107 or QF11. Rule 16(a)(1)(a) states "
Changes to date/time/oneworld carrier/inventory changes are permitted provided ticketed points remain the same". Technically there is no charge for such changes; however, I'm led to believe a carrier is entitled to charge an admin for doing so but, in my experience, AA don't do this. The second option is to push AA to book the TAtl (trans-Atlantic) sector (which in your case is JFK-LHR) on AA. Again, this could be an AA codeshare operated by BA metal.
I am doing SYD-LAX-SFO in order to take the A380 (hopefully business class) . . .
In wich case you must ensure your SYD-LAX flight is on a QF flight number, otherwise it's not possible to request an upgrade (as outlined above).
. . . and then transfer to SFO (not interested in spending time in LAX), is this wise?
Note sure what you mean here by "wise".
Hopefully this is all of some help. If anything isn't clear, just post again or PM me.