Put Churchill on a crate for some backwater in africa between 1940-1942 and have Mountbatten in control sooner. you have your unified india with probably Jinnah as PM actually, i could see some compromise to him not getting his state being that he is the first PM of India(at least at first), probably also if Mountbatten lays down the law that he isn't getting a muslim state, he focuses more on conservatism in India to oppose Nehru and Ghandi who certainly lean towards more socialist ideology (especially Nehru). In that maybe he can bring in some muslim empowerment also, i could also see Nehru gaining some key muslim figures. Politically you would also have parties like Hindu Nationalist Parties (BJP) and a Muslim Nationalist Party eventually come up also.
An All India Party (led by Jinnah) vs Congress (led by Nehru) would certainly make politics interesting at least to begin with.
overall everyone is better off because you aren't forcing people to migrate, resulting in killing and with Churchill out of the picture you would have a more successful Mountbatten.
Not sure how wahabism and india is related. Even with Pakistan its a stretch, the extreme ideology came in because of poor governance and those areas being poor, not because of anything related to Pakistan and India or even Bangladesh as state entities.
The largest cities in United India i would imagine being Lahore (being the main hub in Punjab), Mumbai and Delhi with Karachi not far behind. I think Dhaka is actually smaller since it probably means they would be travelling into other areas and in particular, nearby Calcutta. Without the distraction of forming new nations and still being united, i think they don't have the issue of nationbuilding as such. I think their would be tensions that would come up but you don't have anything fanning the flames so to speak then its probably better for a while at least (well until a nationalist party came in, then maybe cracks really start to show, or if one of the two big parties ignore the muslim/hindu majority areas).
Oh yeah, they'd trash everyone at cricket also.