Buying iphone abroad

Hi guys. I’ve had an Android for the last 2 years, and it’s made me realise how much I miss my iPhone. Anyway.... I’m going to New York next year, and I thought it would be cool to treat myself to an iPhone 11 pro while I’m there. I’m assuming an unlocked phone, direct from the Apple store will work with a UK SIM. My other concern is, if it’s faulty, can I take it to an Apple store in the UK, or does buying a iPhone abroad just over complicate things? Thanks 🙂