1. What extra taxes/fees can I expect, or is the 6750 on the money?
Depends on the issuing carrier. AA is by far the cheapest. BA and QF the most expensive. The difference can be quite substantial...
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?
I would follow the advise above and try for BA. Their membership actually means something. AA is better for redemption though. Depends on what you prefer more.
4. I assume RJ would issue the tickets, as they are the first carrier?
If you use the online tool: yes. But you can get any airline to be the issuing airline. Simply call them in the country you start from. AA would be my suggestion...
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.
Check the hotel section on Flyertalk for amazing deals at Fairmont hotels on Hawaii...
Have fun!
PS: First class is not really worth the extra money given your itinerary.
PPS: What kind of MNL advice do you need?
PPPS: Do not book stopovers as transits. If - for whatever reason - you decide to stay a day or two your ticket will need to be reissued at $125 cost + taxes. Only make it a transit if you are 100% sure you will never change it.