Again, it's hard to generalize but for the modern woman, I think it's no worse than what you'd find in the western world. Until last year, the most powerful politician in India was an Italian-Indian woman (again this might not mean anything but it shows that it's not ingrained into people). Also, given the population, you might hear more cases of inequality. But please don't let that affect your general view of India.
The caste system, I'm very sorry to say this, your ancestors are partly to blame for as well. Like we all know divide and conquer goes a long way in sorting out issues :-). But it used to be societal classification based on one's occupation (and people were free to move across strata as well) which allowed for easy governance. Anyway, today it's pretty much non-existent and is more a class system than anything else (it's a corollary that the highest castes are the richest class today). However, have enough money? Even the highest caste member will not mind handing his daughter over.
The caste system predates the Buddha (500BC) btw. and is routed in Hindu culture.
The British actually also exploited the difference between Muslims and Hindus, but again didn't create the difference. Yes the Raj used divide and conquer, but they used differences that had existed for thousands of years and still do.
The caste system, I'm very sorry to say this, your ancestors are partly to blame for as well. Like we all know divide and conquer goes a long way in sorting out issues :-). But it used to be societal classification based on one's occupation (and people were free to move across strata as well) which allowed for easy governance. Anyway, today it's pretty much non-existent and is more a class system than anything else (it's a corollary that the highest castes are the richest class today). However, have enough money? Even the highest caste member will not mind handing his daughter over.