The heater malfunction is usual for a sensor failure. The heater goes, so the lambda doesn't work very well at low engine speeds, and then if it's too cool, it can collect contamination instead of buring it off, so the lambda sensing elements (just an electrical resistance) can get thrown out.
So, if you're going to change it, that ought to clear up the fault too (though I would remove them prior to changing the sensor, so you can see immediately whether the fault comes back.
I never opened up a lamdba sensor but I guess there's some wire coil/windings to act as the heater. Heaters work by passing a current through a resistance, so if the heat damages the windings that would break the heater. The don't tend to get physically damaged but since they work on a very small range of resistance measurement, anything that upsets the reading can cause problems.
Usually issues come from cheap sensors that are supplied without a plug connector. You have to cut your old wiring and splice the end with the connector on it to the new sensor. Of course, any bad soldering/connection.. or any dirt/moisture in that joint will cause problems later, so it's best to spend a bit extra and get a sensor with a plug attached.
The spacer I don't think is a problem. It looks designed to stand-off the sensor from the exhaust manifold, to avoid heat damage to the wiring. If you remove the spacer, a duff sensor might start working better, since the heater not working doesn't matter, all of a sudden... but longer term, the wiring insulation may melt/short out.. so if Fiat (who might know something about it) went to the trouble of adding a sensor, then it's maybe best if you keep yours on there.
Ralf S.