Asiana does not to my knowledge add any ticketing surcharge for award tickets but any fuel surcharges, taxes and other fees charged by the operating carrier, even if the operating carrier is OZ, will be charged as part of the award ticket. In other words, an award means only a zero cost fare, all additional fees must be paid.
Correct, for most carriers that unfortunately means up you end up paying something around half the price of an economy class ticket in my experience. That's one of the reasons why it makes so much more sense to save up miles until you can get at least business if not first.
In the past, UA has been very generous with its award tickets and I never paid more than a nominal fee of $5-15. This was back when I used UA as my FFP though, so I'm not sure this applies to *A partner awards. Booking awards was the only thing I liked about UA...