A balanced circuit, consisting of +, - (i.e. inverted +) and ground, will reduce even order harmonics.
Ah... I will stir up a lot of contention now I'm sure.
Certain amplifier topologies cancel even-order harmonics that they themselves generate. No amplifier will cancel harmonic distortions presented to its input, since this implies the amplifier can magically detect distortion from wanted signal & somehow remove it.
Put another way, certain amplifier topologies generate less even-order harmonic distortion than others. This has much to do with the internal symmetry (as Analogous said) of the amplifier and not all balanced-input amplifiers are fully symmetrical, and so do not self-cancel these distortions. But balanced input amplifiers that are symmetrical will generate less even-order harmonic distortion than equivalent quality non-symmetrical amplifiers.
The even-order-harmonic rejection is a property of other factors in the amplifier, and not solely on whether it's balanced.
50 and 75 Ohm connections are used for radio-frequency interconnects (and video too). The importance of correct matching here is that the wavelength is short enough that it starts to match the length of the cable. This can lead to standing waves being set up on the cable, which can do damage to transmitters, or rob systems of power - which is important in antenna systems where power levels of a few femto-Watts are being detected.
Impedance matching is generaly not critical in audio since the wavelengths are very long, and signal levels are almost always high enough to make the cable loss negligeable.
What is usually done is to have the load impedance higher than the source impedance, to prevent overloading the source. Overlooking this can give you hassles if you were to say connect a modern cassette deck (input impedance 33k or so) to a tube tuner - which would have been designed to plug into a tube amp, and would expect a load impedance of 1Meg or greater.
On impedance matching, a notable exception is pick-up cartridges and moving-coil microphones.
Both of these have a significant inherent inductance; if incorrectly matched to the load, the configuration results in a filter - and you lose part of the frequency response.
Tube/Valve power amplifiers are also very sensitive to correct speaker impedance matching.
Recording studios and radio stations still stick with 600 ohm references since absolute measuring units such as the dBv and dBm are defined in terms of a 600 ohm load. When absolute level monitoring is critical, you need to know the load impedance precicely. Not relevant to home hi-fi .
XLR connectors are physically very robust, and withstand musicians & roadies stomping on them regularly. But I don't believe that ELECTRICALLY an XLR is any better than a good-quality RCA.