The arrival trace is the same except that OQB's final turn to 300 deg was made a long way away from the usual final turn spot.
The final descent profile and final approach speeds were about the same except that other QF9 had a gradual speed decline from 190kts to 130kts by the time it reached 1000ft. OQB's long final approach started at similar altitude and speed but did not fall below 160kts by the time it descended to 1000ft.
Firstly you need to look at the first approach. It turns base at about the normal position and speed, but then does not descend. So, the "issue" happened just prior to that. The divergence is, of course, the lack of descent on base.
The next approach is longer, which is normal for anything that's non standard.
The aircraft need to be in landing configuration at the time of stabilised approach, so landing gear, flaps, slats would have been already configured for landing. Spoilers would be used to adjust aircraft speed on approach. What is the altitude minima for deployment of landing gear?
Gear goes out around 2,000 plus or minus a bit. The slats and flaps go out in stages. Normally 1 on downwind, 2 on base, 3 immediately after the gear, and 4 around 1,500'. Speed is normally reduced at each extension (to the green dot speed for the configuration). ATC do get involved with some speed management in Dubai, but 185-200k on base and 160 to around 4 nm is pretty normal. After 5 nm, you're looking for Vapp, which is around 135k.
The upshot is that most of the configuration happens much later in the approach than you think, with only the first two stages of slat/flat happening before glide slope intercept. Spoilers are not very effective once the slats/flaps are run, so they are rarely touched on finals, other than to arm them for landing. If you need drag you take the gear earlier. Speed is controlled with power.
My guess is that there was some reason the flight control surfaces could not be configured for a slower landing speed and the pilots needed the extra time to adjust to the new reality and therefore did another "racetrack" lap, and also started their final approach further out.
See, if you look closely you don't need to do much guessing at all. Like everything, there's a procedure to be completed, and you may even be able to carry out a reset, so it's normally good airmanship to discontinue any approach whilst you look at the options.
Would a problem with one of the flight control surfaces result in reversion to a more "direct" law?
No. The more likely outcome is a reversion to alternate law 1, in which case the autopilot is still available.
Interestingly VH-OQB has been unfortunate to be involved in 4 medical diversions - landing in DRW, PER, HNL, SYD.
They probably all have by now.