1. People in the East Asia field will know the universities you are talking about. That being said, I don't think the school level (especially as an international student) matters that much.
2, 3. Have you gotten your MA yet? I'd say you'll probably need some experience demonstrating that you are familiar with not only writing in English but also the English-language scholarship in the field. You'll demonstrate this with a writing sample. Also, looking at your research interest, you'll probably need some Japanese proficiency. Internships and other activities matter much less than your own research experience.
4. Depends on whether you have an MA or not. North American schools don't usually fund international MAs, so I would consider that, too. Also, I would look into getting into MA programs in South Korea possibly with an advisor who is familiar with NA system. You need to be familiar with the English-language scholarship (at least to get into schools you listed).
TOEFL and other things are all supplementary. Some schools have quotas for international students, so good luck.