I'm not related to YC in any way, just an applicant like you. I'm a US applicant, even-though I'm an immigrant and wasn't born here. I'll try to answer some of your questions from common knowledge + my understanding:

1. Getting a US visa may sometime be difficult or take time. My best advice is to get the visa anyway when you can. This way you're ready to come to the interview if and when you're invited.
Visa is just a way of getting here.
Serious candidates are up for promoting their startup in any possible way. Many of these ways go through the US and especially SV (angels, VCs, acceleration programs, the big US market, tech giants, etc). Get it anyway if you can, regardless of YC.

2. I think you actually have a huge advantage as an Indian founder - you have a native access to a huge talent pool and a huge market. Since the ease of doing business in India is at the bottom of the global rank, this advantage is even bigger.

3. No Stripe in India?
Difficult place to do business?
Difficult place to start a startup?
These are real problems. It sounds like a source of many GREAT startup ideas. And Indian founders are, again, in advantage here.

3. As for incorporation, I think it's about what makes sense to your company.
Every place has it's advantages - many big US VC firms fund only companies with a US office while having an R&D and support site in India is cheaper than in most other places.
I'm sure the that folks in YC have good advice about what's right for your company. If you must incorporate already - I don't think that getting incorporated in India will disqualify good candidates from YC.

4. From what I know and read on YC's formal posts, they can't get you a visa. Tourist visa should be enough to get here (it gives you the equivalent of what EU visa-on-arrival gives you, but for 6 months instead of 3). When your company will get US funding over some threshold you should be able to get a working visa. I used to have a tourist visa in the past (wasn't born in a visa-by-arrival country). My co-founder will soon be on a tourist visa, so I know what you're facing.
One of the HackerRank (YC S11) founders didn't get a visa eventually. So his co-founder attended YC in SV and he stayed in India. They kept working hard & on remote during YC. They are very successful today.
DONT let any visa stop you.

5. About your difference from a guy from Boston - you and I are not that different at all. Each of us will leave his place and life if accepted to YC. For you the opportunity may just be bigger and more important, because it gives you full access to the best place in the world to start a startup.

7. Forget about a 'Typical YC applicant'. Be the best applicant and founder you can be, regardless of YC. Their application is built to find great hackers. Graduating from a top US school/IIT can help to demonstrate your abilities, but it's ONLY one way and doesn't necessarily mean you're a successful applicant. Get a founding experience, keep hacking, contribute to open-source projects - all of these help and matter.

Read this blog post by a recent YC grad: https://medium.com/theli-st-medium/hi-im-a-mom-and-a-start-u....
Forget about typical applicant. She made it while having two little girls in LA.
Read her words: Grits, Perseverance, Passion. Not visa, IIT or anything like that.

Msg me if I can be helpfull in anything else.
Best of luck with your YC application!