should I expect the earth to be connected in a UK 3 pin charger?
Not in this case, the shell is all plastic.
I'm guessing I should probably check that the soldering inside the charger looks OK as well?
Check that no soldering is shorting at any point.
check it has a fuse at the point where the wires from the socket meet the board, then you should be OK if there is a fuse
Yes, I would put no faith in the resistor fuse.
Is there anything inherently dodgy about Li-ion batteries that are supplied with Chinese lights, or is it more to do with the act of charging them?
Well lithium is very reactive and when it combusts is does so in a very fierce manner which is hard to put out without CO2 or sand. The charge controller and protective circuit in the blue anonymous battery back is responsible for ensuring that the batteries do not over charge causing fire (or undercharge, reducing the batteries' life). You are basically putting faith in this circuit board and the quality of the batteries themselves.
Although I buy looads of stuff from China every year and have done so since I was a kid, I would not let one of these shink wrapped things into my home personally.