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Just today my battery light came on after waiting forever in traffic. Car has 67000 miles, 06 v7 convertible. I have attached screenshots of codes and I don't think it's making enough voltage at idle. I also noticed at over 200 degrees the fan isn't working. Could a bad alternator cause the fan not to turn on? The fan never turned on. Also the temperature gauge on the cluster has been bad for a while but I can see the temperature on the OBD2 app.
12v at idle and 13v at 3000rpm indicate that the alternator is weak. If the alternator is otherwise in good condition with no bearing noise, you could refurbish your existing unit with a new voltage regulator and brushes.
The engine cooling fan not coming on is a separate problem. If it does switch on when you turn on the AC, the likely culprit is a bad engine coolant temperature sensor. Unplug the wiring harness from the ECT sensor (AC off) and if the fan turns on immediately, you've confirmed the problem.