A question about the sound of corona discharge
To understand the answer to your first question, one needs to start with a voltage low enough that there is no discharge.  This would give you an effective frequency of zero.  As you increase the voltage, it becomes easier to ionize the air, so the frequency of the sound (of ionization) increases.

For the second and third questions... higher harmonics are always present, whether we hear them or not, depends on the sound level they produce.  Since the power level of the harmonics decreases very rapidly, we may be able to "hear" the  second and even the third harmonic, only if the fundamental frequency is loud enough.