"How is it even possible for a single fixed measurer to determine both RSSI and Noise?" - very good question. The noise they are talking about is receiver noise and not interfering signal. At very low powers, the noise is mostly the thermal noise of the receiver: ie, if you were to disconnect the antenna and replace it with a 50 Ohm load (most RF systems are 50 Ohm) you will measure a certain level of noise. So, even if you had all the ideal components, your noise power would be P = k*T*B*G, where k is the Boltzmann's constant, T is the temperature in K, B is the bandwidth in Hz, and G is the gain of your system. In reality, every component adds noise as specified by its noise figure (listed in the datasheet of every RF component).
If you look again at the noise power equation, you will see that by reducing bandwidth, you also reduce the noise. However, high bandwidth is necessary for high data rates, which explains why you need good SNR for high data rates.
"Why both values are negative and measured in dBm" - 0 dBm means the power is 1 mW. -20 dbm means the power is .01 mW. The minus indicates the number of dB below 0 dBm. Without the minus, it would have been above 0 dBm
"But who radiate that power?" - in case of noise, it is internal, in case of signal, the transmitter. However, fundamentally it doesn't matter.
"But why is its value so small then?" - it comes from what is called Friis transmission formula. So, with several simplifications, imagine that my transmit antenna radiates power isotropically in all directions. So, your power is uniformly distributed on the surface of a sphere of radius r (and surface area 4*pi*r^2), where r is the distance from the transmit antenna. In Imagine, that your receive antenna is about 1 m^2 and it can capture all the radiation that hits its surface. Now, it can only capture 1/(4*pi*r^2) of all the radiation, making the receive power very tiny and RF engineering a complex field :). This is a very hand wavy explanation but I hope it makes sense
SNR as you know means Signal-to-Noise ratio. So it's \$20 log(\$\$V_S\over V_N\$), where \$V_S\$ is signal voltage and \$V_N\$ is noise voltage. So, if noise (\$V_N\$) is really small (compared to signal), then SNR gets really big.
It's quite possible to have systems with negative SNR (where the signal level is less than the noise), where you need synchronous demodulation or a lock-in amplifier to pull the signal out of the noise. In that case, you could write Noise-to-Signal ratio \$20 log(\$\$V_N\over V_S\$), which would be equal to - \$20 log(\$\$V_S\over V_N\$).
GNSS systems such as GPS have a negative SNR before processing.
Best Answer
There's two things to consider with a preamp which explains why it improves SNR.
The first, and most important, is that the pre-amp is closer to the source (such as a microphone). There's fewer noise-generating components between the microphone and the pre-amp than there would be if you waited all the way to the main amplifier. For example, quite often there are treble/bass knobs between the pre-amp an the amplifier to adjust the tone of the sound. These devices add noise, but because they occur after the pre-amp, they're adding noise to a 1V signal from a low-impedance source instead of adding noise to the tiny signal that comes from the high-impedance microphone.
The second advantage is that it's easier to do clean amplification at low currents/voltages. It's much easier to do the amplification in two steps: one step raises it from the tiny signal from the microphone, and the other takes that signal and powers the speakers. In fact, it's likely that if you didn't have a pre-amp before your tone controls, you would likely have a 2 stage amplifier (which is a pre-amp and main amp slapped together).