Electronic – Unbalanced to balanced audio signal conversion

No, that's not what he does. He feeds each microphone through an amplifier then through an output impedance that feeds the line through R14 and C4 shown in thick red circle below: -

I've shown the wire that is the actual line used by the intercom in a thin red/brown circle.

Because of the output impedances of several units connected all at once there will be no clash of signals and, within reason, the line voltage will be an approximate sum of the contributions of all active intercoms.

AC coupling via C4 is needed for the op-amps but note that there is a call circuit that needs to put DC onto the line to "ring" the other intercoms.

Side-tone cancellation takes place around U2B and for a 1-to-1 call you won't get feedback in your ear of your own voice. With several of these units connecting at once you may get feedback from mic to ear and this could cause havoc to other users too. So be aware of this.

Balanced Line out with DC signalling: -

In theory, no connection to the center tap of the primary is actually needed. The "balanced" signal is differential, so only the voltage difference between the two lines matters. The transformer inherently works as a differential front end, since only voltage across its input coil causes and magnetic field that is the coupled to the output coil.

However, you don't want the common mode voltage of the balanced signal to go too far from ground. If totally insulated, it could pick up static electricity and build up to 1000s of volts, eventually arcing over something and causing a crackle sound in the audio. The resistor provides a relatively weak path to ground, but it's plenty low enough to prevent static buildup. The capacitor does the same thing but more so at higher frequencies. At too high common mode frequencies, the inevitable capacitive coupling in the transformer will cause some of the common mode signal on the input to show up as signal on the output. The capacitor provides a more serious connection to ground for AC, while the resistor only a weak connection for DC to avoid ground loops.

Note that since this connection to ground is halfway thru the primary of the transformer, the magnetic field caused by the common mode voltage across one half the winding is offset by the magnetic field caused by the common mode voltage across the other half of the winding.

Personally, 22 µF seems really high to me. I would want to let the common mode float more easily at audio frequencies. I would have been more concerned about squashing the pickup of radio station, while letting pickup from the power line be a common mode signal that the transformer should do a nice job rejecting. The two halves of the primary aren't going to balance exactly, so you don't want to push more common mode signal thru there than you have to.