1, on your terms, you should definitely be free of tuition. Anything with a professional counterpart will do.
2.BK2 1 Scholarship is actually not a form of individual application, but depends on whether some research institutes of key universities in Korea can apply for BK2 1 scholarship support. If you apply for all BK2 1 scholarships, you can get a monthly subsidy.
3. The monthly subsidy for BK21scholarship is about 200,000-400,000 won/month, depending on the allocation of professors and the number of students.
4. You can try to apply once first. Your education, language ability and achievements are outstanding. If it is not ideal this time, prepare new TOEFL scores and TOPIK scores at the same time, and try again next time. If you have an IBT of 100, plus Band 6, I suggest you apply to Seoul National University.
Scholarships in Korean universities are not decided by professors, at least at the time of admission. More according to your comprehensive conditions, judged by the admissions office. In fact, after entering the school, you can get a higher scholarship through the recommendation of the professor and your own efforts.
6. yes. It will be difficult to apply for this professor in this school in the future. Of course, it depends on the personality of the professor and your wording. It's basically not good.
To tell the truth, the comprehensive strength of local national universities is not too strong. Among the national universities in Korea, except Seoul National University, Busan University and Gyeongbuk University, they have a certain position in fame and ranking, and others are even inferior to many local private universities. As I said before, if you can further improve your language performance, apply to Seoul National University. You have this ability. And don't worry about tuition, work hard to earn some living expenses. Seoul is not impossible.