Yes, you absolutely must apply in R1 if you are Indian. To do anything else is a waste of time and money.
I really don't believe that this is true at all. Applicants spend far too much time worrying about this kind of thing and not enough time strengthening their own applications. Schools expect to receive more apps in R2, and they plan accordingly. They have NO incentive to lie to you and tell you otherwise.
To your question #3, an applicant from India is probably viewed the same, whether he lives in India or in the U.S. I doubt there's much difference there, although I may be wrong.
Naturally, you're asking these questions because there are tons of similar applicants who all want to get into the top ten schools. The most effective way to overcome this problem is to make your application as strong as possible, not to game the system.
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