Having done this flight a few times now for F Lounge runs

, I can answer these questions....
1. Check-in only opens 3 hrs beforehand, or at least that is the earliest it will open up. Special priority lane is only for Star Class passengers. QFF status pax get no priority; you cannot use the QF F check-in even if you are Star Class and/or QF WP.
If airside time is a big thing for you and you are not travelling Star Class, I recommend lining up at the counter as soon as you can.
2. You will get a boarding pass with an orange D sticker attached to it. The D sticker records details of the photo identification you presented at check-in (e.g. drivers license, passport, etc.). There is a special lane at immigration for D stickers and APEC people - you can use that lane if the other lanes are moving too slowly. They will stamp the D sticker in SYD as well as incoming in MEL.
Note that you do not need a passport to travel on JQ35 SYD-MEL, but you do need photo ID. Immigration procedures are not expedited any faster with or without a passport.
3. No web check-in. You can register a preference for your seat - of course, no guarantees.
4. Boarding commences 40 minutes before departure - this is the textbook definition. I recommend moving towards the gate at around this time if not a bit earlier. This is not one of those flights you want to run for - especially since it usually docks at the Star Alliance concourse (i.e. the farthest one from the QF lounges!) Shuttle buses between the
oneworld and Star Alliance concourses are available at gate ~26.
5. By rights you can if your incoming flight to SYD is on QF or
oneworld. Truth be told I haven't tried this yet, especially since the incoming SYD flight and JQ35 are on separate itineraries, but reading the "rules" on the QF website (Sydney T1/T2/T3 airport information), this is what I construe from it. You will probably need a copy of your JQ35 documentation and/or your incoming-to-SYD BP.
Other notes:
- Since this leaves from an international terminal, liquids etc. rules apply. Quarantine laws also apply when you touch down in MEL (so don't be surprised if sniffer dogs are parading around), but you do not need to fill out any immigration cards (i.e. green (outgoing) or orange (incoming)).
- One part of the JQ BP will be taken at the gate at SYD; the other part will be taken at customs at MEL. So you will have no BP after you travel this route. If you need to keep the BP for any reason, you should consider taking a photograph of it once you receive it in SYD. A photocopy in the QF lounge works just as well.