Regarding RC Phase Shift Oscillator
The system theory provides an answer to the question (pole location, quality factor, solution in the time domain,....) .

However, without going deep into system theory, the questions can be answered as follows:

A.) Loop gain LG=1 means that the damping in the feedback path is fully compensated by the gain of the active element within the loop. That means: The amplifiers input signal Vin produces an amplifier signal at the ouput Vout which will be attenuated by the feedback network exactly down to the level Vin. (The amplifier produces its own input signal in conjunction with the feedback path). However, this must apply to one single frequency only.

(a) Note that LG=1 means: |LG|=1 and phase(LG)=0 

(b) For LG&lt;1, the gain is not large enough for compensating the attenuation of the feedback path - and the oscillation amplitude (if existent) will continuously decrease.

(c) For LG>1, the opposite will happen and the amplitude will continuously increase until it will be limited by the hardware (supply voltage).

(d) Very often, such a hard-limiting is not desired (harmonic distortion) and an additional non-linear element is used for "soft-limiting" (diodes, FET as controllable resistance) .

B.) Lowpass vs. Highpass.

As always in electronics, each solution has some advantages and some disadvantages. Therefore, depending on some application-oriented requirements a tradeoff is necessary.

(a) Three lowpass R-C sections: The lowpass provides attenuation of harmonics produced in the amplifier. However, the input resistor Ro of the inverting amplifier loads the last R-C section and must be included in the calculation.

Solution: (1) Ro>>R, (2) Additional buffer amplifier, (3) Best solution: Only two R-C sections and one inverting integrator instead of an inv. amplifier.  

(b) Three C-R highpass sections: The last (grounded) resistor (Ro) can be combined with the input resistor of the following inverting amplifier (gain: - Rf/Ro). Hence, no loading error caused by the amplifier. However, the highpass network is noise-sensitive and cannot provide damping of harmonics.   



C.) Regarding the phase: Three R-C (resp. C-R) sections are required to allow a total phase shift of 180 deg at one single finite frequency (the inverting amplifier gives additional 180deg phase shift to fulfill the oscillation criterion with 360 deg). It is not allowed to use a formula which applies for one single unloaded stage only. We even cannot say that each section would provide 60 deg to the overall phase shift of 180deg. This would be only true in case of isolating the sections from each other.