Sorry I've forgotten most of my Japanese so I'll write in English instead.
1) The requirements for undergraduate admissions are at http://www.nus.edu.sg/oam/apply/international/admissionreq/BYA-admissionreq.html
Since there are no national qualifications for high school students in Japan, I believe you will also need SAT I and II.
どういたしまして。。anyway, I called the admissions office to ask for more details.
I hope my understanding of the Japanese system isn't wrong, so just to be sure, you should double check to make sure that you have none of the qualifications applicable (e.g. International Baccalaureate).
If that is the case, then you should take SAT I and II and in this case you will NOT need TOEFL (since SAT I will cover English).
oh yes.. and during your application you should mention any achievements if any. the business school website (http://bba.nus.edu/admissions_requirements.html) states that:
"Up to 10% of vacancies will be set aside for consideration of exceptional candidates for admissions to NUS. For such candidates, other factors besides grades will be taken into consideration. They should provide details in the "Discretionary Admissions" section on the online application form. Some examples of exceptional achievements that the University may take into consideration are:
Medalist in any of the International Olympiads (Biology, Chemistry, Informatics, Mathematics and Physics)
Winner at the National Science and Talent Search
Representative for Singapore in Arts and/or Sports events
Active participation in community service and volunteer programs
Work experience relevant to the course applied for
Key leadership positions in community organizations, sports and athletic clubs (outside school)
Entrepreneur who has started and managed a business
Participation in the NUS Business School Young Entrepreneurship Challenge"