Dear Armin,
Thanks for your message. I am happy to know that you find my Essay fun to read. Concerning your questions:
1. Actually, the permittivity of free space is not present in Eq. (2). I added it when introducing Planck units for the sake of completeness. The quantity 2pi in the RHS of Eq. (2) comes from the relation between the horizon area A and the mass of a Schwarzschild BH, see this technical paper for details.
2. No, it works for both of them when they will start to emit Hawking radiation.
3. In general, QNMs emit gravitational waves. Also the recent detections by LIGO are partially due to QNMs in the ring-down phase of the final BH after the merging of the initial ones. But QNMs due to Hawking radiations are too small in order to emit detectable gravitational waves. In any case, neither stellar nor super-massive galactic BHs are currently emitting Hawking radiation. They will start to emit Hawking radiation when the temperature of the cosmic background radiation will became minor than their proper Hawking temperature, that is, in a very very distant future.
Thanks again and good luck in the Contest.
Cheers, Ch.