vlt,
Are the destinations listed just for the 1st RTW trip you are planning?
As Christep has mentioned there are a plethora of LCC's that operate within SE Asia which, if you need to get around in between the likes of KL, HK, BKK and SIN will provide sufficient means of transport for a very, very competitive price - Although in my experience you need to book tickets 30+ days in advance to take advantage...
It looks as though the only reason for going to HKG the second time is to get from KUL to SIN? If so, then it'd be far more convenient to look at Air Asia as they operate out of KUL, or consider taking one of the 'VIP' busses, which take about 4-5 hours to do the journey.
As for South America, a routing of SCL-LPB//LIM-GRU-EZE-SCL would allow you to visit many of the sights you've mentioned you wish to see - the major excepetion being Easter Island which will require 2 spare coupons (Which, as mentioned by christep you could purchase providing your itinerary totals less than 18 segments thereby keeping within the 20 segment limit once you've purchased the SCL-IPC-SCL flights) You could do La Paz to Cusco overland via the Salt Flats and Lake Titicaca then get a cheap flight (circa US$110 one-way) from Cusco - Lima.
From Lima you could head to GRU, which would be a good base to see the Falls and Rio, albeit both are in seperate directions, return flights to GIG are pretty cheap using TAM. You'll need to head overland to see the falls. BA have a flight from GRU-EZE which is part of their LHR-EZE service. Then the short hop from EZE-SCL. You could of course, do this in reverse order.
To also save the hassle of going ATH-BCN-IST-MAD (and helping reduce segments for the S.America bit) you could always go from LHR-ATH, then go via the Greek Islands to IST overland/sea/air, i'm not sure if it will be quicker to go to IST via Spain having not done the journey before, however i suspect despite the reputation of Greek/Turkish relations there must be a cheap air, or ferry service to IST?!
As for crediting to FF Programmes, i have no idea. But luckily many people here are experts of yielding as many miles out of a trip as is feasibly possible.
I've just got back from my first RTW and than planning stage as exciting as it was turned out to be frustrating as the more I looked into different destinations, the more destinations it seemed i wanted to visit... But it is ultimately very rewarding.
Good luck, and happy planning!