Sounds similar to life in Dhaka in the 1980s. I remember many sleepless nights where the power went out for no discernible reason and our air conditioner (a window unit in my parent’s bedroom) stopped working. My understanding is that this has gotten much better in Dhaka over the last decade, though the recent energy crisis set things back.
I once spent most of the summer in a WW2-era building with no AC in the southeastern US (Ft Benning). I imagine it is both hotter and more humid in much of India.
Short answer is that you get used to it. There was a surprisingly effective swamp cooler that worked about half the time (we got pretty good at troubleshooting it) and several ancient pedestal fans. You can sleep in very nearly any environment once you become sufficiently sleep-deprived.
