I'm usually hanging out on Star Alliance, but for this trip it looks like OW is best for me, with multiple flights on LAN.

Tentatively (Jan/Feb):

MUC-AMM (few days in Petra / Dead Sea)-RJ
AMM-HKG (via BKK) - RJ, CX
HKG-MNL (looking for some advice for the Philippines) - CX
MNL-HNL (via NRT) - JL, JL
HNL-DFW (side trip planned out to Arizona) - AA
DFW-EWR - AA
EWR-SCL (via MIA) - AA, LA
SCL-PUQ (two days in Punta Arenas) - LA
PUQ-SCL - LA
SCL-IPC (two days on Easter Island) - LA
IPC-SCL - LA
SCL-FRA (returning to Germany, via MAD) - LA (one flight number)

Looking at doing this in Business, and the OW RTW planner says it is legal, 15/16 segments, and 6750 Euro (4 continents).

1. What extra taxes/fees can I expect, or is the 6750 on the money?
2. I don't have the actual mileage tallied up (not sure if the OW RTW planner does this?)
3. I have base membership in LA and BA. I would like to obviously use this trip to get some kind of status with either. Does BA assess tier points for non-BA flights? I know LA does, but you need to fly a certain number of segments on LAN?
4. I assume RJ would issue the tickets, as they are the first carrier?
5. I've never been to Hawaii, but generally don't like big cities to hang out in. Any ideas for a 'quieter' island? I was looking at arranging a flight to maybe LIH on Hawaiian.

Thanks for any advice or thoughts. As stated, first RTW so I'm not too familiar with this yet.