Welcome to FT Yolalon and congrats on your first post. Taking a RTW trip is an excellent way to celebrate redundancy IMHO.

To answer your questions:

1. No. Oneworld Explorer base fares do not vary. From time to time they are raised, more or less in line with inflation.
   
   In particular, there is no price variation depending on how close in to your departure date you decide to purchase your ticket.
   
   However purchasing close-in to departure might mean you have problems with availability, especially in economy class and more especially in economy for flights such as SYD-SCL-IPC-SCL for which finding availability is always difficult.
   
   The small variations in total price that you have seen as you tried various itineraries will be because of differing taxes, fees and charges for the flights and stops.
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2. In theory you can purchase a Oneworld Explorer from any Oneworld airline, however only the first airline in your itinerary is obliged to sell it to you; other airlines can refuse and many of them will if you have no flights with that airline.
   
   In your case, to purchase with BA you can simply have your first flight (LHR-HKG) with BA (or you could fly LHR-BKK direct with BA).
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3. You don’t say which FF programme you would accrue to. All your flights can be accrued to the one programme, but economy class earning can be quite poor, as low as zero on some flights.
   
   Business class earning is better, but in my experience the ‘value’ of the FF miles earned comes nowhere near to offsetting the incremental cost of business class over economy.
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4. It is true that the competence of airline telephone agents varies considerably when it comes to making changes to these tickets. In my experience it always takes at least 30mins to get even a simple change done (hence I always use Skype to telephone!). I’m always put on hold while the agent verifies that (a) I’m allowed to make the change, and (b) in the case of date changes, that there is no charge. I’ve found BA is reasonably OK, and I’ve read reports on FT that CX is OK too. (the one exception I’ve had is the AA RTW desk; they know the rules and I once got a date change done is less than 5 minutes!)