I can't answer all your questions, but I just deplaned from BA001 3 1/2 hours ago, so I can add some thoughts:

You can check award availability (and book) on ba (select the stopover option, to address another of your questions). Check out www.britishairways.com/spendmiles and log in. There's even a discount right now for booking online (unless it expired 8/31) IIRC, it's 5000 points on US-originating flights, 2000 on flights from LHR.

I booked my flight using QF miles, but I referred to the BA site to check availability before I called QF.

P.S. I didn't see any celebs, so today isn't a good one for that