If India wasn't partitioned

National
1. India might have still lost the 1962 war
2. The civilian democracy would have still survived
3. The nation would have become strongly federal

International
1. The USA would have found it difficult to support Afghan Mujahideen
2. The communist dictatorship in Afghanistan would have survived
3. The Soviet Union would have lingered bit longer
4. The Taliban would have never been created
5. The 9/11 might not have happened
6. The ISIS wouldn't have been there

Social
1. Hindutva wouldn't have grown so strong
2. The Babri Masjid would have survived

3. Linguistic faultlines would have been exacerbated

4. The Muslim birthrate would have come down quicker. The present-day Pakistan region  would have had a smaller population than present-day Bangladesh region
5. Conversions to Christianity and Islam from the caste system would have been higher
6. Many regions with 30% Muslim population would have been close to 50% because of migrations and conversions
7. There would have been stronger OBC and Dalit movements

About prayers

I guess one could distinguish between acceptable prayers and unacceptable prayers as one would do between acceptable bribery and unacceptable bribery.

Here prayer is for the future gains or thanking the deity for any gains.

Acceptable:
1. sickness
2. fertility
3. impending fatal danger
4. clearing an exam

Unacceptable:
1. surviving an accident in which many others perished
2. for jobs
3. for better grades
4. more money

Basically, anything where the believer is the only beneficiary is acceptable, however, in situations where it appears as if god/s has/ve to take sides praying is unacceptable. One shouldn't put limits on gods for the greater good of the society.

Of human behaviour

There is a thinking that human society progressively improves. But the present situation where the right-wing is in ascendence makes one wonder. Many Sci-Fi TV serials or movies show that the basic human nature is consistent and never transcend even after amazing technological innovations. So, our imagined future as depicted in Science Fiction or the reality where the right-wing is getting away with atrocious statements and deeds tells otherwise. I wonder whether we need to disassociate human society from human nature.

I may not be able to define basic human nature. I'll put them into the following categories.
1. Humans with criminal tendencies(or selfish streak) who can be part of all the classes and who can harm the society for their benefit
2. Humans in survival mode who probably form most of the lower and middle class and probably majority women, and who generally maintain the status-quo though always under the impression that they are doing good
3. Humans defined by the puritanical definition of "good", can be anyone from an Islamic fundamentalist to a Vegan activist, who can bring radical changes to the society by generally suffocating it
4. Humans with individualistic streak who can be part of all the classes, who are always a positive influence on the society but lack the resources and mindset to sustain it

Typically, the nature of the sedentary human society was decided by the males from the groups (1) and (3) and sustained by the conflict-weary group (2). This is known as patriarchal or feudal society. Now, most of the societies have become liberal or culturally socialist societies. This was achieved by the coming together of groups (4) and (2).

But what we can observe that group (2) isn't a reliable group. Their survival instincts can be manipulated easily. As the oppression by the feudal society is a thing of past, they can no longer associate inhumanity with the patriarchal ideas. This has allowed groups (1) and (3) to regain power.

However, the laws of the society have been successfully changed for the benefit of the majority in many cases during the socialist interlude. Now, the new feudal power can oppress minority populations(which itself can be divided into all those four groups) while maintaining group (2)'s sense of security.

Basically, the new laws are responsible for the continuous evolution of the society in a positive direction. However, majority humans within that have continued to be in the same mental attitude as their forefathers.