The thing is, if India hadn't been split up, it probably would have emerged IMO a "regional imperial power" like how China did OTL (able to seize Tibet and push around Vietnam and manchuria and N. Korea and even India and stuff like that). The British, unwittingly or not, with the creation of Pakistan (and the subsequent splitting of Pakistan into Pakistan and Bangladesh) did a traditional divide and conquer method, leaving an India encircled by enemies and hence unable to play an active role outside its immediate region.
An heir to the Mughal crown...probably not as South Indians wouldn't care and the Sikhs would be POed and so would the Marathas (no Bombay!). Then again, it just might work, if he did some sort of grand thing to make people love him. IMO, Gandhi would have been the best candidate for such a post. Nehru had a humongous ego and was at the same time idealistic in the extreme, which IMO made him a brilliant freedom fighter but a somewhat disastrous leader of a country.
The Soviets cared more about Persia than India as Persia had oil and Indian Ocean access and wasn't as far away or as well armed as India. India also would be more full of resentful people than Persia should it be occupied or made a satellite. Also, most Indians could have cared less about the Soviet UNion.
CHurchill trying to hold onto India and treating both Jinnah and Nehru badly and basically saying "screw partition, screw independence, your ours now and ours forever" would have really killed any ideas of partition as an drive for independence took over. This would do it IMO. As for Afghanistan joining, I don't see it happening as they are IMO a fiercely independent people and also because in much of Indian (and Pakistani) literature and conventional wisdom, they get a pretty bad rap at times. Then again, it might happen far off into the future if the "United Indian Republic" is doing well.
And there's little reason why it shouldn't. Asia's best infrastructure post-WW2 (japan and CHina bombed out and India's huge rail and road network), ports like Calcutta, Bombay, Madras, and Karachi, democratic gov't, lots of natural resources and raw materials if nothing else for export, local sources of wealth (Tata corporation and other family-owned, Zaibatsu-like setups, the princes, etc.) and a well established English-speaking upper class would certainly help provided things aren't f**ked up by Nehru going down the Socialist route he went down in OTL.
If India is an economic superpower by today, it would look more like Brazil (large gap between the rich and poor) than Japan (more evenly spread out wealth) unless it somehow manages to bring its population growth under control. Perhaps land-reform and earlier emphasis on family planning might do the trick?