I am planning to go to India in February 2017.
Note: Due to so many regulatory changes happening since Demonetisation of old 500 and 1000 Rupee notes, you might have to research again for any new announcements made by the RBI, the day/week prior to your travel.
How much money can I exchange at the airport as per current regulations?
As per this circular made by the RBI, the limit for exchange of foreign currency into Indian currency is INR 5000 per week at any currency exchange center be it at the airport or in cities, provided, you submit a self-declaration that you haven't made any exchanges in that week.
Will I have any trouble in getting hold of Indian currency at the airport?
Not if you oblige by the rules mentioned by the CBEC, India and exchange restrictions imposed by the RBI (mentioned above).
What alternatives do I have for exchanging money while in India?
You can use ATMs, as the withdrawal limit has been increased up to INR 10000 as per revised rules resulting in smaller queues.
Also since merchants and hotels have adapted to new conditions, you can use online payment wallets like PayTM, FreeCharge, MobiKwik to pay them. Also for travelling you can use UBER and OLA, which let you make payments using your cards and online payment wallets.