iPhone bought in China mainland couldn't get Apple support in

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Contact – Official Apple Support

The staff in China were incorrect.

You will have to have it serviced in China.

Did you call the British Apple Support number?

We aren't Apple on this user to user only forum. But you don't have a battery issue with your iPhone. Batteries are consumable parts and with every full cycle charge of the battery, it's health will decline and there is no way to stop that. It's what batteries do. ALL BATTERIES. As muguy correctly suggests, a decline of 1-2%/month decline is normal and Apple won't replace the battery under warranty unless its health declines to 80% or less in the first 12 months, which you are most unlikely going to see.

一丁16 wrote:

But the problem of declining battery health is accompanied by the problem of charging heat and stuttering. Is this normal?

Yes, once the battery is past it's useful life, all sorts of things will go wrong.

Once your battery health decreases to 80 percent, have it replaced. Batteries decline by 1-2 percent in health each month, your battery seems to be in that normal decrease.