Yeson Center accepts USD, but other stores will usually accept credit card, even small stores, or korean currency. We had a flight arrival at Incheaon airport, which is a bit far from the city, about an 1 1/2 drive with the Bus and went out with a departure at Gimpo. But usually it is Incheon unless you have a stop in Japan or China (we had one in Bejing). Jessie from Yeson can tell you recommended Hotels close to the Clinic. But you will be at the clinic only 3 times, so it is not really that much of an issue if you choose a different hotel that is not in Gangnam of all expensive places 😉 - And only one of the three times it is needed to take a taxi, that is the day of surgery. Other than that, the subway is your friend, faster and cheaper than taxi. Seriously, we took more time with the taxi to Yeson from our room than with the subway because traffic in the rush hours is insane.
When writing to them, keep in mind that there is a time difference and they may read the email a day later and then you read the reply another day later, if they replied instantly. If she does not reply within a week, I would just try again, usually I always had a reply within a few days unless I asked something where she had to ask Dr Kim himself, then it took much longer at times as it depended on when he had time for email consultations.