1

If you're talking about an Indian sim card, no. And not that terribly easy to get one that will continue working in India - as a foreigner. Can be done, takes patience and a bit of cleverness.

2

With valid documents like passport and visa u can get the sim card. There are many options as all are major telecom operaters still prefer to but Airtel, Idea or Vodafone in the same order.

3

We spent a couple of months in India last year, and had the most frustrating experience getting a smartphone SIM card. I think we bought 2 that didn't work at first. Third one worked, but it took over24 hours to have it activated, and several trips back to the store until it was all straightened out. A month later, it was deactivated, and it took several trips and many, many phone calls to sort it out again. It seems that every state in India has its own contract, so if you bought in one state and are now in another, you're in trouble. I hope things have improved and you will find it easier! Fortunately, I brought along an ancient flip phone and the sim I bought for it worked great. I used that phone dozens of times a day, and used wifi n guest houses whenever I needed to research something.