I will accept much of your post but have these points to make :
1. The Aryans migrated into South Asia not before 1000 BC.
2. There was a question in last week's Kaun Banega Crorepati. It was about a village ( or maybe it was region ) in Himachal which was said to have one of the world's oldest democracies and the question was which king's descendants do these people claim to be. The answer, which I had guessed correctly, was Alexander the Great. And what was this democracy ? It was most certainly brought by the Greeks. The idea called Demokratia - direct democracy though flawed in its version but a milestone nonetheless. So Hindus had lot of influences from non-Hindu cultures and this I would say would be in astronomy ( and astrology ), artistic expression, mathematics, probably medicine and probably clothing too ( like the sari ).
3. About the Mahabharata, some days ago the Pakistani member
@firohot4321 said that this epic was a derivation of the Greek epic Iliad.
There reversed roles of devas and asuras notwithstanding it is certain that original Hinduism originated in Iranic lands and then the Hindus probably had some cultural tussle with other Iranics and then migrated into South Asia around 1000 BC and who knows what they did to the IVC ( if it was still existent then ). The Hindus probably then adapted their religion to local environment.
@Aryzin, what is the understanding in Iran about the Aryan Hindus who migrated to South Asia ? Also I must mention that our Parsi member
@padamchen calls Hindus as his cousins and many years ago had posted about cultural similiarities between Zoroastrianism and Hinduism like the Torana decorative and luck-bringing string-and-leaf arrangement hung over the main door.
I don't think modern Sanskrit is the origin of that word. Must be some Iranic language from which Sanskrit borrows.
Good info.