Did it overheat because it was low on coolant and was it low on coolant due to failing head gasket?
If it isn't using coolant it could be blocked radiator.
If it isn't using coolant it could be failed water pump.
1) I'm not sure why it overheated. It surely wasn't low on coolant. Radiator didn't work at that time, that's for sure. Why didn't it work remains a mystery.
But now it seems to be starting at 100C, which I thought could be a little too high, but apparently it's normal.
2 and 3) Not sure what you mean by "using" coolant -- did you mean coolant flowing, or coolant disappearing?
I'm not sure whether it's flowing, but it's level stays the same. No leaks, etc. (and I think a pump would leak if broken).
But I am considering looking at the pump too.
By the water movement in the reservoir I can confirm that there didn't seem to be a flow at 94C (at which stage the thermostat should be open I think). Unless the flow is so weak that can't be spotted...
One more fact: when the fan is ON the coolant temperature drops, it can drop to 70C easily (if I disconnect temperature sensor, at which stage ECU indicates error and starts the fan) --- which means it is flowing through the radiator I think...
So I don't know whether it's flowing or not any more... shouldn't water movement in reservoir be apparent?
Everything could be already working as expected, but I'm just trying to understand how could the engine heat up to 135C; even with a failed fan this shouldn't have happened. It was 20C outside and I was on the motorway doing 70-90mph, so there was plenty of air flow through the radiator. It was 4 of us in the car, which could cause some more load on the engine... but that much load? I don't know... :/