Recently I have heard that the Magento Payment System is non-compatible with the South Korean market, and basically, that I will need to build a website/store using a completely different platform in order for it to work in South Korea. Is this true? Are there extensions, or otherwise, that allow safe and efficient payment in South Korea?
Thanks for your help
Perhaps, you have to find Magento solution partner in Korea.
I don't know which company is the best in your country, but maybe someone will assist you.
This issue is not only your country, but also most of Asian countries.
Actaully this is not true at all, we here at Seoul Web Design build a number of payment extensions for South Korea such as CNS pay http://www.seoulwebdesign.com/product/lg-cns-pay-magento-2-korean-payment-extension/ for both magento 1.x and version 2.
We are also technical partners with the KG INICIS and LG CNS pay the leading payment gateways in Korea and can assist with merchant account setups.
Please feel free to drop me an email for any more questions you might have, email@example.com