Hey! You might be interested in a recent answer of mine dealing with Mughal mechanisms of managing their diverse society. There is definitely more room for discussion here though, especially regarding your first question of how peaceful the regions of South Asia (it's difficult to talk of India at that point in time) under Mughal rule were. If you have follow-up questions I could try and add to them, as soon as possible.

Here is the short version of my earlier answer:

The Mughals were successful for quite some time at managing an empire that incorporated various ethnic and religious groups, for reasons both unique to their context as well as connected to older traditions. First, their religious policies should be seen as drawing on Islamic precedents that made relative religious freedom of the subjects (while paying special taxes) possible. Second, policies such as Akbar's reliance on Hindu civil servants have to do with Indian “Realpolitik”: As a Muslim empire with a large Hindu population and with neighbouring Hindu realms whose powers varied over time, the Mughals had to in some way accommodate Hindu influences. This drawing on local elites was standard procedure in many other parts of the world, e.g. in forms of European expansion. [...] In addition to these social changes connected to exterior influences, the Mughals [...] starting with Akbar also took up an expensive program of cultural patronage, accompanying religious diversity with a mixing of influences from Islamic and Hindi arts. The results from these programs had a legitimising function as well in that they communicated the successful “syncretism” taking place that was connected to the Mughal rulers' religious “charisma” to the outer world.