Not quite sure I understand your second remark about the phase margin, so a circuit such as this would not work if built in the lab?
I also did want to mention that the calculations above mean you can work out R and C to produce any Sinewave generator you want from the formula, you just need to know the typical Gain response of the Op-amp you're using. However I can't quite see a way of going in the other direction, i.e looking at a circuit and figuring out it's oscillation frequency from R and C. To rearrange my formula to calculate F, it is still a function of R, C and the Open Loop gain of the Op-amp, which itself is a function of frequency A(f). However, how do you get A(f), when you're looking for F in the first place? Puzzling. You could of course use the values of R and C to define the attenuation of the RC filter response and substitute its reciprocal in for A(f). But again, this is also a function of frequency. Going around in circles a bit!
Megamox
As to your 1st question: The circuit given by you resembles a circuit called "differentiator" for an input signal applied to the capacitor (lift the ground of course). It is just the inverse of the classic MILLER integrator. However, as you didn`t change the pole distribution by applying an input signal the circuit will still oscillate and - therefore - cannot be used as intended. It is still an oscillator! And - by definition - an oscillator has a phase margin of zero deg (loop phase 360 deg).
Thus, you have a circuit that is intended to be used as a differentiating amplifier. However, it cannot be used as such because it (probably) oscillates.
As to your 2nd question (calculation of Fo for given R, C values).
First we need some theory. The circuit oscillates only if the loop phase is 360 deg. The feedback lowpass always provides a phase shift slightly BELOW 90 deg. Thus, the opamp must provide a phase shift slightly ABOVE 90 deg. This is possible due to the second opamp pole.
Thus, for a correct loop gain calculation we have to use a 1st order lowpass and a second-order gain function resulting in a 3rd-order loop gain low pass function. That`s quite normal since a pure 2nd-order lowpass reaches the -180 deg shift at infinite frequency only.
However, a much simpler approach is possible as you have assumed already in your former post assuming that BOTH parts contribute with 90 deg phase shift (because the cut-off frequencies are much lower than the operating frequency).
In this case we simply can set (GBW=wT=transit frequency):
Opamp gain A(s)=wT/s and low pass H(s)=1/(1+sRC) >>> 1/sRC.
Then we have a loop gain T(s)=- A(s)*H(s)=- wT/(s^2*RC) and with s=jw we get T(jw)=wT/(w^2*RC).
Now, the circuit oscillates for |T(w=wo)|=1 leading to
wo=SQRT(wT/RC) .