People didn't massacre each other because a new political border had been created, they did so because they hated each other, and the end of British rule gave them an opportunity to act upon their hatred
There was nothing wrong with the Partition of the country, the way it was done was a disaster. You could have an organized population transfer of people who actually wanted to move and there was a lot of people who wanted to move. There was a complete break down of law and order.
. A united India would just have given the Hindus more victims to oppress.
This is just pure laziness in analysis, oppress? how? In United provinces Muslims formed 14 percent of the population but 50 percent of it's police force was Muslim, a huge portion of the Military was Muslim, remember a disproportional number of troops opted to go to Pakistan. The whole Marshal race thing did put, certain Muslim communities, not all since all Muslims in south Asia are the same some fared well under the british rule some did not, on an advantage. The same can be said of the civil bureaucracy, certain communities were disproportionally represented which is why here in India we have a programme of affirmative action so as to ensure this crap does not repeat again and in the army there was forced integration of the army and the community based regiments now a days are just name sake ,basically the concept of Marshal race in India was destroyed. British did divide and rule not only between religions but within castes, religion and ethnicity.
So explain to me, how in a united India would Muslims be oppressed? they had significant representation in the military and police and even the bureaucracy. This is just a very lazy analysis. In fact partition destroyed the Muslim communities in south asia as their accumulated social and economic capital was split between two and later three countries. The Hindu communities on the other hand consolidated in what is today India. Which is why partition was the worst thing that happened to the Muslims in the long run. Which is why south Indian Muslims are way better off than their north Indian counterparts because they did not have their communities ripped in to two or three parts.
India will have to be more decentralized that OTL, so large states like Bengal and Punjab don't use their influence in parliament to take advantage of their smaller neighbors
You need to change the nature of the Indian Independence movement lead by the congress. All factions of the congress be it may secular or Hindu right or Socialist or Capitalist or centrist or liberal or conservative, did agree on how India should be run, as a centralized state with states given significant regional autonomy within a framework put forth by a strong federal government. They were inspired by a very colonial notion that a divided Hindu India was weak and thus fell prey to foreign invasion so the solution was a centralized state like the Mauryas, the one Indian state that defeated the Greco-Iranian empire in the west.
You had partition because you had Bengali, Sindhi and Panjabi elites complaining about the program of the congress and it is not a surprise that it was in those states that congress had the least support and Muslim minorities in other Indian states did oppose a strong federal government. This fear was embodied in the Pakistan resolution or the Lahore resolution and quote:
That geographically contiguous units are demarcated regions which should be constituted, with such territorial readjustments as may be necessary that the areas in which the Muslims are numerically in a majority as in the North Western and Eastern Zones of (British) India should be grouped to constitute ‘independent states’ in which the constituent units should be autonomous and sovereign.
Look at the language, we often talk about religion but we do not talk about as to how the congress's desire for a strong central government was causing tension in the minds of the elites in these provinces that later became Pakistan, religion is just half the picture. of course their fears ended being misplaced as India went from being a hyper centralized state at it's creation to a decentralized federation now a days with very strong cultural autonomy to its different people and Pakistan went the opposite route for a while.
Most violence around that time happened in states that were being divided by British or princely states that had to choose between the two states
In other states the violence was never that extreme.
true, you could say it was non existent.
Given that India today has 200 million Muslims without collapse into civil war (that is not to say there are not severe issues) I do not think it inconceivable a United India can exist. You need only have the secular current for independence come to leading prominence around figures like Bhagat Singh, for example.
It's hard, but doable.
communist India? Bhagat singh was a staunch communist, I don't know if that would be a good Idea.
Given that the Hindus and Muslims were already fighting and killing and ethnically cleansing before hand, I think the hope of two different communities living together is - unlikely.
That is blowing it a bit out of proportion. Riots? Sure....Lynching? .....sure... but ethnic cleansing? that's a strong word, i mean I am not saying Hindus and Muslims lived peacefully, they lived separately, an average Hindu would go his entire life without meeting a Muslim more than 10 or 15 times, and all of those encounters would be with the authorities and same goes for Muslims. Which is why you did not have cleansing for about 300 years, since the mughals collapsed.
I am pretty sad that nobody mentioned separate electorate! like that seriously divided the leaders of both communities and disincentivized the political leaders of both communities from forming common grounds. Congress leaders were apathetic to the demands and fears of the Muslim community and Muslim leaders played to the fears of being a minority in a Hindu dominated India. Again the blame lies in the hands of the british, they did light the explosive, not saying the explosives wasn't there in the first place, they did light it though. 
