Why did Buddhism become the dominant religion of Asia but phased out of India? Did the Hindus copy the Buddha?

Also, if you know this subject, please explain:

Which came first Buddhism or The Gita?
Did Hindus phase out Buddhism?
Do Indians respect the Buddha?
Why do Indians promote Islam over Buddhism?
Update: S, I have seen often Indian leaders and movie stars etc only talk about Hindus, Muslims and Christians in their speeches ... even after your attacks by Muslims on 26/11. They never include Buddhists ... never. Also I read an article that Hindus were upset that Buddha was against the caste system and so I believe... show more S, I have seen often Indian leaders and movie stars etc only talk about Hindus, Muslims and Christians in their speeches ... even after your attacks by Muslims on 26/11. They never include Buddhists ... never. Also I read an article that Hindus were upset that Buddha was against the caste system and so I believe the Brahmeens tried to get rid of the Hindus. Also many people believe that the Gita was written after Buddhism in order to revive Hinduism. Please do not insult me for no reason for these are very valid questions.
Update 3: I mean this article shows that the Brahmeens tried to phase out Buddhism. I am not taking sides, I am just curious :)

http://rupeenews.com/2008/02/03/why-did-...
Update 4: Thanks everyone for your great answers! Also Dharma I'm not sure what you mean but I am not speaking against Hinduism and would never do so. Ever since my close friend introduced me to these eastern religions I am very fascinated. I did not mean any disrespect. Another user called Kathmandu posted this link and... show more Thanks everyone for your great answers! Also Dharma I'm not sure what you mean but I am not speaking against Hinduism and would never do so. Ever since my close friend introduced me to these eastern religions I am very fascinated. I did not mean any disrespect. Another user called Kathmandu posted this link and so I wanted to see what other Indians thought about it. Thanks for your detailed answer .. wow! you know a lot :)
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