SAT

Hi Tanmay,
The chances are pretty strong with 90%. Being 17 years will not be an issue. If you had a gap, you must simply justify your gap period - how you spent the period, the activities you were involved in, etc. However, entry requirements are different for both the universities and you must check the website well before applying.
For NTU, 90% is the minimum percentage requirement, so admissions are going to be competitive. Though, SAT or ACT are not required.
In case of NUS, if you are from a state board you must take the SAT or ACT. However, CBSE and ICSE board students need not take SAT or ACT.
Weightage will also be given to the LORs and SOP. So, prepare well and write to the universities for specific information.
Good luck.

The application process for SAT and TOEFL is online, you need to visit the official websites for registration, test schedules, test prep materials etc. Please check https://collegereadiness.collegeboard.org/sat and https://www.ets.org/toefl for details.
You will be eligible to apply to MIT after taking the SAT and TOEFL, however whether you will be considered and admitted is up to the university and depends on a number of factors such as co-curricular activities, academic standing, achievements and overall profile. Visit the MIT website, check the undergraduate admission requirements and process and what they look for in an applicant. Good luck.