now I come across with some problems in China using local carrier, everything is working properly except sending text message, and iMessage and Facetime also seem not to work.This is very serious for Apple
No, it simply is not.
Your device is not unlocked. Paying full retail does not mean unlocked, it simply means you paid full retail.
Contact Sprint to get the device unlocked, if you meet their requirements.
Then use the device with a supported carrier.
There may still be issues with SMS, but that is a carrier feature.
As for iMessage and Facetime, they should work. But as you've provided no details of what "not working properly" meaning specifics of the issue, no one here can really help you.