Welcome ame_ to Flyertalk, and welcome in particular to the BA forum. And goodness what a question (which I have to admit largely falls outside my knowledge base). But thank you for joining us here, and given such an interesting itinerary I very much hope you will continue to post here.

The only comments I can make is that (a) I think you'd be very lucky to get all of that with Avios, availability for some of these sectors is very low indeed; (b) in the first question, the BKK and JFK example is two tickets since you return to London; (c) in practical terms I can't see any agent being able to find availability to be able to ticket this in one go, it seems inevitably a split reservation.

I also suggest that using a oneworld explorer ticket, particularly a DONE in business class, may prove very economic and relatively easy to book - you use need to find D bucket availailability and there's a handy tool on oneworld.com. But not with Avios or indeed the companion voucher.