If I buy iPhone 15 Pro without choosing any carrier will it be unlocked?

If you buy directly from Apple, Yes. It would be unlocked even if you choose a carrier.

The only time an iPhone from Apple comes locked is if you choose AT&T's installment plan to pay for it. In that case it is locked to AT&T.

No. Warranty is only valid in the country of purchase.

Your brother would need to somehow take the iPhone back to the U.S. for Warranty service if any is required. Or send it to you and you take it into an Apple Store directly.

Apple will not take international shipments for service.

As Mentioned, the US iPhone 15 models, only supports eSIM. It has no physical sim slot.

That means in India the iPhone can be used with Reliance Jio, Airtel and Vi only.

click here ➜ Find wireless carriers and worldwide service providers that offer eSIM service - Apple Support

There is no international warranty on iphones. Even those repairs that are possible to have done outside of the country of original sale are pretty much impossible to have done in India.

If the phone will be used in India, buy the phone in India.

No, if you purchase the phone in the US, the warranty will be valid only in the US. Also note that all US models will be equipped with eSIM capabilities, but no Nano SIM slot.