Generally, you must be a native speaker in theory
to teach in S. Korea. But, immigration will (or has been) grant(ing) E-2 visas to non-native speakers with both of the following two criteria:
1) The teacher has a passport from one of the following 7 countries: Australia, Canada, Ireland, New Zealand, South Africa, The U.K., The U.S.A.
2) The teacher has a degree from one of the above countries.
You mentioned that you
Got my education(Masters in Science) in the States
So, if you send your degree from the U.S. and if you have a Canadian passport, you can obtain an E-2 visa to teach in S. Korea.
I'm not sure about China or Taiwan, but I've heard that you can teach in Taiwan without a degree...
Good luck with your future plans!