For the low Cat stuff to be useful, you need, the airport to have the right equipment, the aircraft to be so fitted, the crew to be qualified and current. Plus, you will also need some sort of alternate, that does not require an alternate itself. That last part could well be the hardest bit to provide where Perth is concerned. Busselton may have become useful since I retired, but last time I flew into Perth (in a 747 quite a long time ago), the state was pretty devoid of alternates.
All of QF's long haul flights aircraft are 111a or 111b, but I don't think the 737s go past Cat II (AV?). In a career that was mostly long haul flying, I've done lots of Cat II, a few Cat IIIA, and one or two Cat IIIB.
Yes. And it wasn't the only diversion that was subject to question at the time. There was another in the vicinity of Alice Springs, where they diverted to Melbourne after an engine failure.
That just means the runway is long and concrete.
I'm not sure whether it was a commercial or competence decision. In either case it was a stupid choice. They'd have to be close to #1 on my list of people not to fly with.