How did India join the Soviet bloc during the cold war? Excellent answer! But I have to disagree on your point that USS Enterprise was present & was ready to help India. This Wikipedia article says the exact opposite. "December 11: Liberation of Hilli, Mymenshingh, Kushtia and Noakhali. USS Enterprise is deployed by the USA in the Bay of Bengal to intimidate Indian Navy."
How did Islam and Hinduism thrive together in Medieval India? India or parts of it was under Muslim rule since 1206 (Delhi sultanate), about three centuries before Mughals came. So co-existence cannot be completely explained by Mughals being tolerant.