OZ will pass on whatever fuel surchages that the operating carrier impose. EYs surcharges are relatively small compared to other airlines, but will be applied.
In my experience the fuel surcharges for Etihad are not charged by Asiana Club. LAX-AUH has a $1k YQ in ITA but Asiana agents quote ~$20 as taxes and fees - the trouble is to find an agent who knows how to find EY availability - most will come back with 'not available' for any request (i doubt they actually check). Hold times are very long currently.