The rad fan controls are very different throughout the Stilo engine range. 1.8, JTD and 2.4 engines have the same controls but all the rest are different so be careful if you're searching posts for answers
With 1.8 engines then there are no relays and you have a separate fan control ecu next to the radiator (bad place to put sensitive electrics) so they are more often the cause of problems
Your fuses are F6 and F16 for the fan control unit called M150
First thing i'd check is whether the fan control unit is being told to turn on by the engine ecu. Signal arrives at the fan control M150 on connector C on pin 2. If there is no signal voltage there ( and I would suspect that there isn't) then the fan control ecu has a problem as it is turning the fan on without being told to by the engine ecu
If there is a signal voltage there at C pin 2 then the ecu is telling the fan to turn on and you'd need to find the reason why. Could be the air con linear pressure switch or engine temp sensor
But it's much more likely to be an internal fault in the fan control unit M150
If you remove F16 then the fan should stop but I wouldn't advise leaving leaving it out. Better to have a over cooled engine than a cooked one.
Fan control unit M150 is quite expensive and if you search you'll find some people have managed to resolder the unit internals or simply obtained a used one