Originally Posted by Gearhead Jim

And to answer the original question-

No one knows if your battery is causing these issues, but it's well known that a C6 will start to do all sorts of goofy things if the battery is getting weak.

The voltage you read with the engine running should actually be the alternator voltage, as controlled by its regulator. So the voltage reading is only vaguely related to the condition of the battery and can vary considerably under normal conditions.
Most auto parts stores will test for battery for free or a nominal fee.