Hi
Apple Watch Series 3 (GPS + Cellular) is not locked to any specific carrier and has a built-in eSIM that copies information from the iPhone's SIM card.
The built-in cellular features require a carrier plan for your iPhone in your country of use that specifically includes support for Apple Watch Series 3 (GPS + Cellular), including the carrier activating the device on the plan.
In order to use the built-in cellular feature in another country, you need to have an Apple Watch model that supports the relevant LTE and UMTS bands for your intended country of use and your supported carrier there.
There are three different regional versions of Apple Watch Series 3 (GPS + Cellular), each supporting different LTE and UMTS bands, as detailed here - Apple lists different models for the US and the UK:
Apple Watch - Carriers - Apple
Note also that EE is currently the only UK network to support this feature.
If in doubt, I suggest that you contact your intended carrier to ask whether any given model can be used on their network with a plan that they may offer or plan on offering for iPhone that supports Apple Watch Series 3 (GPS + Cellular).
Apple Watch Series 3 (GPS + Cellular) can instead be used without activating the built-in cellular feature, in which case it functions like a GPS-only model, in conjunction with an iPhone 6 or newer model of iPhone (running the latest version of iOS) and a service plan from any carrier.
The built-in cellular features cannot be used when roaming.
The warranty terms for an Apple Watch purchased in the US are detailed here:
Apple One (1) Year Limited Warranty