Can anyone check that the following is a valid business class RTW itnerary with OW.

Melbourne - Bali
Bali-(Hong Kong)-Osaka
Osaka - Hong Kong
Hong Kong - (London) - Beirut
Beirut - London
London - Oslo
Oslo - (London) - Barcelona
Barcelona - Quito, Equador
Guayaquil - (Lima - Santaigo) - Lima *
Lima - (Santiago) -Rio de Janeiro
Rio - Santiago
Santiago - Easter Island
Easter Island - Tahiti
Tahiti - (Sydney) - Papau New Guniea
Papau New Guinea - Melbourne

* Any other way of doing Guayaquil-Lima or Quito - Lima

I think this means that i have to buy 2 more segments? (Europe & South America)

Do I get full miles with BA?
If not, what miles program should i enroll in?

Thanks

Jupeter