I'm not going to address the production mechanism,1 just the nature of the "sound" in this case.
What you think of as the hard vacuum of outer space could just as well be seen as a very, very, very diffuse, somewhat ionized gas. That gas can support sound waves as long as the wavelength is considerably longer than the mean free path of the atoms on the gas.
As for the tone, there is a simple relationship between the tone of the same name in different octaves, so once they know the dominant frequency they can figure its place on the scale.
1 Though it won't be happening inside the event horizon -- which is where "not even light can escape" holds -- but in the region around the hole proper where it accumulates gas and dust and the magnetic fields from the hole play merry havoc with the ionized components of the accumulated stuff.
There are numerous misconceptions here, but allow me to address just a few:
Black holes do not have "appetite." In order for an object to be consumed by a black hole, the object's trajectory would need to literally intersect with the event horizon (i.e. be on a collision course with it), otherwise the object will continue to orbit the black hole. Because black holes are extremely compact, it actually makes it relatively difficult for orbiting objects to fall in. Instead, objects might come close to the black hole, and be accelerated to relativistic speeds, which accounts for the energetic phenomena that we observe in the vicinity of black holes.
All of this applies to Sgr A*. Despite how massive it is, it's also very compact. This makes it a relatively rare event to observe a star (or a gas cloud) actually falling into it.
We observe a large cloud of antimatter in the galactic center...
The "cloud of antimatter" to which you refer is not a cloud of antimatter, but a cloud of matter with a smattering of positrons that is slightly greater than elsewhere in the interstellar medium. It's also not quite centered on Sgr A*. For a much more complete answer on this subject see https://physics.stackexchange.com/a/111758/10334.
The universe is expanding with an accelerated speed. This requires energy to be added, and if energy pours in through white holes, energy is added.
...but we don't observe any energy "pouring in" from Sag A*. Furthermore, we know that the repulsive force of dark energy is uniformly distributed throughout space, and not localized to centers of galaxies.
We have never observed any singularity, so why should a black hole
singularity exist?
The singularity is, by definition, hidden inside the black hole, which is why we can never observe it.
Best Answer
The accretion of matter onto a compact object cannot take place at an unlimited rate. There is a negative feedback caused by radiation pressure.
If a source has a luminosity $L$, then there is a maximum luminosity - the Eddington luminosity - which is where the radiation pressure balances the inward gravitational forces.
The size of the Eddington luminosity depends on the opacity of the material. For pure ionised hydrogen and Thomson scattering $$ L_{Edd} = 1.3 \times 10^{31} \frac{M}{M_{\odot}}\ W$$
Suppose that material fell onto a black hole from infinity and was spherically symmetric. If the gravitational potential energy was converted entirely into radiation just before it fell beneath the event horizon, the "accretion luminosity" would be $$L_{acc} = \frac{G M_{BH}}{R}\frac{dM}{dt},$$ where $M_{BH}$ is the black hole mass, $R$ is the radius from which the radiation is emitted (must be greater than the Schwarzschild radius) and $dM/dt$ is the accretion rate.
If we say that $L_{acc} \leq L_{Edd}$ then $$ \frac{dM}{dt} \leq 1.3 \times10^{31} \frac{M_{BH}}{M_{\odot}} \frac{R}{GM_{BH}} \simeq 10^{11}\ R\ kg/s \sim 10^{-3} \frac{R}{R_{\odot}}\ M_{\odot}/yr$$
Now, not all the GPE gets radiated, some of it could fall into the black hole. Also, whilst the radiation does not have to come from near the event horizon, the radius used in the equation above cannot be too much larger than the event horizon. However, the fact is that material cannot just accrete directly into a black hole without radiating; because it has angular momentum, an accretion disc will be formed and will radiate away lots of energy - this is why we see quasars and AGN -, thus both of these effects must be small numerical factors and there is some maximum accretion rate.
To get some numerical results we can absorb our uncertainty as to the efficiency of the process and the radius at which the luminosity is emitted into a general ignorance parameter called $\eta$, such that $$L_{acc} = \eta c^2 \frac{dM}{dt}$$ i.e what fraction of the rest mass energy is turned into radiation. Then, equating this to the Eddington luminosity we have $$\frac{dM}{dt} = (1-\eta) \frac{1.3\times10^{31}}{\eta c^2} \frac{M}{M_{\odot}}$$ which gives $$ M = M_{0} \exp[t/\tau],$$ where $\tau = 4\times10^{8} \eta/(1-\eta)$ years (often termed the Salpeter (1964) growth timescale). The problem is that $\eta$ needs to be pretty big in order to explain the luminosities of quasars, but this also implies that they cannot grow extremely rapidly. I am not fully aware of the arguments that surround the work you quote, but depending on what you assume for the "seed" of the supermassive black hole, you may only have a few to perhaps 10 e-folding timescales to get you up to $10^{10}$ solar masses. I guess this is where the problem lies. $\eta$ needs to be very low to achieve growth rates from massive stellar black holes to supermassive black holes, but this can only be achieved in slow-spinning black holes, which are not thought to exist!
A nice summary of the problem is given in the introduction of Volonteri, Silk & Dubus (2014). These authors also review some of the solutions that might allow Super-Eddington accretion and shorter growth timescales - there are a number of good ideas, but none has emerged as a front-runner yet.