Can I purchase a device in the US and take it to Belarus without an issue?

The only lock you'll find are the following:

iPhones purchased in the US are dual eSim only, so your carrier MUST support eSim or it won't work as a phone there.

Only Apple sells fully unlocked iPhones, so if your relative buys it ANYWHERE other than Apple it won't work in Belarus at all.

iPhone does NOT come with International Warranty. If the phone breaks or needs service support, it will HAVE to be brought back to the US for service and it cannot be shipped, it has be physically brought back to the US.

A far better option for your relative would be for them to send you the money you need to purchase the phone in your country, where it will receive support and work there.

As long as you understand you'll have NO warranty on a phone purchased in the US, you and your relative take your risks.