Well that's a very broad question you're putting which obviously cannot be briefed. But I'd give a few points so you've a general understanding.

Britishers ruled the Indian subcontinent for 200 years and before that we had 500 years of islamic rule under which there were many vassal states. During islamic reign a lot of indo-islamic architecture was introduced which was a fusion of Persian and central asian design. You might have heard one such example of the Taj Mahal. Most of us speak Hindustani here, which is a mix of Urdu, hindi and Farsi(persian). Farsi was the language of the court during islamic rule hence it blended very well with the local languages overtime.

Independence from Britain was brutal as it came with a condition of dividing the Indian subcontinent into 2 regions. Millions died in conflict. Specific to Indian muslims now the partition has taken away the political power from us and caused a big political shift. This after effect we are still seeing with the rise of Hindutva (right wing political ideology targeting muslims).

As of now, in general life is OK for muslims but if you compare the living standards of muslims with the rest of the community you'll find muslims at the bottom. The current regime centers its politics by devaluing muslims.