If you go to Harvard’s International Statistics website (http://www.hio.harvard.edu/statistics) and enter STUDENTS, HARVARD COLLEGE (the undergraduate school) and INDIA, you will see that there are currently 20 students from your country enrolled at the college. That means, on average, about 5 students are admitted every year from India.
Harvard doesn’t publish the number of applications from each country, but my guess would be close to 1000 students apply to Harvard each year from India. If I’m correct, that would mean the overall acceptance rate for students from india students would be about .05% (one half of one-percent). Those are terrible odds no matter how qualified you are, so by all means apply but realize and understand the tremendous odds you face.
It would be fine to take the SAT w/writing in October and the Subject Tests in November.