FaceTime, iCloud and iMessage in China

FaceTime, iCloud and iMessage are location-independent. The location of the sender or recipient does not affect the price you pay to use the service: free.

However, how you connect to the internet may cost. Using free Wi-Fi will be free, or you can pay roaming rates to your SIM card provider for cellular usage, or you can purchase a Chinese SIM card and pay a provider in China. This is payment for connecting to the internet, to use any service, not specifically for any Apple services.

You should not change your iPhone region.

In general, there is no need for you to change your iPhone region when travelling overseas.

As @grgarside already mentioned, whether you will be charged will depend on the Internet connection type. However, using a high speed Wi-Fi over data is preferred for FaceTime calls.