if I buy an Apple watch in USA with GPS + celluar can I use the same in India with India Airtel or any other Carriers

Each carrier listed has a specific Apple Watch model number. The model numbers for U.S. Apple Watches will be different than the model numbers for India. But you will find that the model numbers for India are the same for many other countries.

But note, the warranty is NOT international, so buying outside of India may not be able to get warranty service unless returning to the country where purchased.

Not all countries support all features, so you want to make sure the country where you buy has the same feature set as India

https://www.apple.com/watchos/feature-availability

The GSP+Cellular Watch from the US does not have the proper hardware for India. He would need to model Watch that is compatible with the India carriers. Not all of the carriers support the cellular Watch either, that is why there is a list of carriers that support the Watch.

No. If you really want to gift your cousin a GPS+Cellular iPhone, your best option is to give him a gift card for that amount.

Yes, It should work. I bought mine (S5 two years back) and its been working great.

~S