Nothing in the airport arrivals area I'm afraid. However, if you drive out of the airport you'll find several stores .. none of which are likely to be open at midnight.
You might wait for the next morning and buy it yourself from almost anywhere in the city (you'll see shops with signs advertising Airtel, Vodafone <- new name for Hutch, Tata Docomo, Uninor etc etc SIMs), or if you've scheduled a pickup from your hotel, you can have the hotel concierge send you a SIM along with your driver. If you want the SIM to be in your name you can just fax / scan + email them your details.
Yes - passport + 2 photos should do the trick.