Free WiFi seems to be available in almost any place. So you can probably use Skype.

I don’t think you can get a prepaid cell SIM card. Korean phones are proprietary.

If you want to call back to Singapore, I’d recommend walking into any convenience store and saying 국제 전화 카드 하나 주세요 (Gukje jeonhwa kadeu hana juseyo) — please give me one international phone card. Most of those cards cost 5,000 or 10,000 won and have a lot of minutes on them.

If you want to make a call in Korea, you can buy a prepaid phone very cheaply, maybe 30,000 won, and set up a prepaid account by showing the ajeosshi your passport and giving him 10,000 won, but that will be a very small number of minutes, not suitable for calling Singapore.

the cheapest way to call is through yahoo messanger. that is what i have. i call to the usa all the time. they have international phone cards to. so you will be okay.