No-Contract iPhone X and Upgrade Eligibility

Hi All!

I'm interested in buying a no-contract iPhone X (paying full price) as a gift for a relative oversea. When I'm on the Apple.com site, it asks me for my AT&T account (I assume this is for eligibility checking?) Since I'm not upgrading my phone or anything, will buying the phone for a relative impact my upgrade eligibility (let's say I want a new phone 3 months down the road)? How do I get it to be unlocked for international usage? Do I wait 2 months or 14 days?

Thanks!