Taking unlocked iPhone 16 to India

One of my cousins in India is requesting parents(who are here in the US) to bring a brand new iPhone 16 Pro from the US. It seems it is cheaper to buy in the US vs buying in India is her take.

I do have some questions before I spend money 1000 plus on this. Could someone who has done clarify my following questions

Would she be able to get an esim in India and use the phone. It would be an unlocked iPhone 16 Pro. I hear that esim is needed at the time of phone activation itself.

Should I buy Applecare given this situation of buying in the US and using it in India permanently?

Anything else I am missing.