First of all,I said Alexander lost dearly in India .I never mentioned abt his death.
Aryan invasion was a myth.I will not take that in to account.It was not an invasion but was almost a `sublimation’.
You said Abt Muslim ruling India for 1000 years.Pls understand the fact that Muslims did not rule India as a single force but there had been many Muslim rulers and kingdoms and they were fighting each other.Simeltaneously,there had been Hindu rulers aswell.If you are trying to say about Mughal dynasty,my friend it had been just a comic one after Aurangazib and the last rulers were not bigger enough to cast any kind of influence.they were repeatedly atatcked by Jhats,Marats and others.
Now you are talking abt partition … If that’s your logic,pls see the developments after 1947.We have 1971 also and we Indians(Hindus,Muslims,Christians,Sikhs and all others) could divide Pakistan .
Portugese and French have caused considerable infulence on Indian Subcontinent history .They were not any of Tom and Dick class.It was portugese only who ended centuries old Arab sea trade monolpoly.They indulged in forceful conversions,displaced thousands of Goan Brahmins from their aborogin land,Caused considerable impacts on Kerala history,they had their share of trade and other diplomatic affairs with Mughals so what’s more u need to establish their impact?
French had their share of impacts on India.Its evidence is Pondicherry.
jews.well India is one of the only few places where they could live peacefully.A simple proof is that a few years ago israeli prime minister thanked people of Kerala and its rulers for safe guarding Jews and their interests. 
Finally,pls understand that India is the only place, or one of the few places in the world,where all the so called `invaders’ were literally forced to become a part of the Indian mainstream.