Can USA iPhone 14 Pro work with Indian carrier?

It will work on an Indian network IF it is provisioned w/ an eSIM.

However, only three (3) Indian carriers are currently listed as being able to provision an eSIM.

Find wireless carriers and worldwide service providers that offer eSIM service - Apple Support (CA)

No, if your carrier in India requires that you use a regular SIM card. Do they?

Otherwise, the only information that we have regarding the use of eSim in India would be in this document:

Find carriers around the world that support eSIM on iPhone

Currently, the only carrier listed in this link that would support eSIM is Reliance Jio.

If this is not your carrier, you should not buy the iPhone in the U.S. Buy the iPhone in India.

Yes.