Bruce Farquhar wrote

Those cheap Chinese water heaters which are simply two plates
of metal, one on live and one on neutral, how can they work?

The current flows thru the water and that heats it.

Because the resistivity of tap water apparently
varies from 2 to 200 ohm metres. That's a
range of 100 fold in possible power output.

That only affect how long it takes to heat the water.

I assume the resistivity changes due to
impurities like lime in hard water areas?

Yep.