LUPO 1.4 – Air conditioning is not possible – Thermoswitch for fan, thermostat or encoder G62/G2 defective?

Hello, I hope that someone can help me with the logical thinking, because I am now completely confused… First the symptoms: 1.) Air conditioning does not cool, when switching on the air conditioning I hear a cracking (magnet switch?), but the radiator fan does not start as it should. 2.) Temperature indicator in the instrument cluster only works once in a while after starting off, pointer then goes after about 1 km again to zero and does not come up again even with longer rides. Diagnostics until now: 1.) According to air conditioning tester there was enough coolant in it, there was also no pressure loss detected. Nevertheless, I can not rule out that the combi switch G62/G2 has a double function now: G62 gives info to the motor control unit, G2 to the combi instrument. So if the indicator does not work out, probably G2 the combistat should be broken? Then I have read the problem again.