First, just a point of maintenance, it's Asiana Airlines, not Air Asiana. Also known here on FT as OZ, their IATA code.
I believe you're ok with OZ even if you never fly on their airline. Their criteria for Star Gold is pretty good compared to most. One thing to be careful of, and please check before committing to OZ or any other program is minimum segment or mileage requirements to qualify for status. United is 4 segments on their own flights, ANA is 50% of the miles for the status level, many airlines have such a requirement.
As for spending miles, you may have to call in for awards, but any Star Alliance flights are eligible subject to routing rules and *A award availability, etc. I've never used OZs award search so don't know how it is for online awards on partner airlines.
Something else to look at that's more in your region is TK (Turkish). Their qualification and re-qualification is also pretty easy, but redemption is more difficult. If you're ever flying on certain cheap TK fares that's the only place to get mileage credit.
You'll be paying tax on all airlines. Fuel surcharge is a different story. Using either OZ or TK, you'll pay fuel surcharge on most redemptions.