Hi there and welcome
Yes, the Verizon models of iPhones (all of which are unlocked) will work on any carries using GSM in the US and international. Whether or not they will work on a CDMA carrier in China is a different question. Generally, CDMA providers only allow phones on their networks that were sold for use on their network. Also, some carriers in China use what's sometimes called "WCDMA". That wouldn't be supported. I would consult the Chinese carrier for more information as it will differ per carrier.
It is always easiest to go with GSM as this is the most commonly used standard internationally.
But yes there are some countries that do not use it, but by far the majority is GSM
Previously not as it was built in but now it is more common they use a UICC/CSIM card, similar to a SIM card. But having one does not guarantee it works on all carriers as the carrier needs to allow the phone.
If you would like any additional information or assistance, please do not hesitate to let me know.
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yes, they are becoming popular, even Verizon has started using them