Can we purchase AppleCare in India for MacBook Air purchased from USA?
Apple recommends you to purchase an AppleCare protection plan in your country of residence, implying the country where you'll be seeking repair services.

Support - AppleCare - FAQ - Apple (IN)


Where can I purchase the AppleCare Protection Plan?
The AppleCare Protection Plan is available at the Apple Online Store and many Apple-authorised resellers and wireless service providers.

To answer your questions:


Once I purchase the laptop from US and come back to India, will I be able to purchase AppleCare for this laptop here in India?


Yes.


If yes, will there be any restrictions on the AppleCare?


No.
P.S.: The answers are based on information provided by Apple and from personal experiences.