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Just go with the basics:

1) Here is a massive opportunity

2) Here is the awesome founding team

3) Here is why we will be the ones to win this huge opportunity

4) Here are some proof-points (e.g. customers, product development, etc.) that back us up

YC goes out of its way (like to Vancouver!) to find the best startups in the world. If you can nail those 4 things, it doesn't matter where you're from.

Ashu fellow Indian Founder here. I think it's mostly about dedication, domain expertise(if applicable), progress and traction. They list it out here http://www.ycombinator.com/howtoapply/

you will never get an answer to "what do YC partners look for". And we as alums dont really know - we have some ideas, but I'm pretty sure they are not accurate.