Can I buy a local sim card
Yes but generally a local sim is going to be expensive for calling home. Local sims will be prepaid and they are not usual suitable for international calling. You also need time to purchase one and this might not be possible at the start of your team.
Your home country sim will probably be expensive to phone home with to. Check at home with your service provider. If you’re going through Hong Kong you can get sims that operate in both regions. Text messages are probably most economical. To avoid unpleasant surprises when you get home and see your bill you should check your mobile data roaming costs with your phone service provider before leaving home.
In China there is an app called WeChat. We recommend downloading and trying to install that before you leave home. It will make contact inside the team much easier.