1) Yes. You can fly AA LAX-LHR and BA LHR-EDI. The only BA miles that are not counted in the AA program are across the Atlantic so the rest of the BA flights you take will count.
2) Best route is probably LAX-LHR-EDI-LHR-HKG-LAX or LAX-LHR-EDI-LHR-NRT-LAX with the latter being a bit shorter but the former will let you fly CX which, in the opinion of many here, is equal or better than BA and is definitely better than AA. You could go via SIN but there are no direct SIN-LAX OW flights so you would end up going to HKG or NRT from SIN to get back to LAX.
3) If you don't get comp'd to AA Platinum you can take something known as the Platinum Challenge. Your proposed RTW will qualify you for Platinum when you hit HKG or NRT. As I haven't flown AA business across the pond, I'll leave the comparison to DL BusinessElite to others.
4) The mileage via NRT is about 17,500 and via HKG is about 19,300. If you fly business you get a 25% bonus (50% for first). Plus, once Platinum, you get a 100% bonus. Thus, if you go via HKG you will end up with about 31,000 miles.
5) A three continent RTW (NA-Europe-Asia-NA) will work fine. In business from the U.S., it will cost $6,200 plus tax and airport fees. However, if you originate in YVR you can save about $1,300. You can still terminate in LAX, you don't have to return to YVR. One possible problem is that you cannot commence your return from Asia earlier than 10 days after your departure to Europe.
[This message has been edited by ExMo (edited 12-27-2002).]