Electronic – the unit for resonant frequency

The Q and M curves show that the resonant frequency is a property of the transformer, the load and the series capacitor. \$f_o\$ isn't necessarily a 'shorted' resonant frequency but a mostly-load-independent second resonant point predominantly controlled by the leakage inductance and series capacitor.

The switching frequency is indeed controlled by the some form of control IC (usually a PWM). The frequency of operation will vary as a function of input line and load, and should stay above the worst-case (minimum load) resonant peak to ensure ZVS over the whole range. You are correct in that operation below the worst-case peak gain forces the converter into an uncontrolled region and should be avoided.

LCD TV and laptop adapters are usually < 24V. If the designer was able to use a schottky diode for the output rectifier, you don't have to rely on forced commutation from the primary to reduce losses. The best way to tell if you're suffering from excessive reverse recovery loss is to put a current probe in the secondary and measure the reverse recovery current. Operating this 70V converter above resonance means they're not soft-commutating the secondary (which isn't necessarily bad) to reduce conduction losses (less circulating current in the primary).

Find the input admittance

$$Y = j\omega C + \frac{1}{R+j\omega L} = j\omega C + \frac{R-j\omega L}{R^2+\omega^2 L^2}$$ $$Y = \frac{R}{R^2+\omega^2 L^2} + j(\omega C + \frac{-\omega L}{R^2+\omega^2 L^2}) $$

Then the Resonant Fequency is when the Imaginary component of the input admittance is zero$$Im(Y)=0$$

So $$\omega C + \frac{-\omega L}{R^2+\omega^2 L^2} = 0$$

$$\omega C = \frac{\omega L}{R^2+\omega^2 L^2} $$

$$\frac{C(R^2+\omega^2 L^2)}{L} =1 $$

$$\frac{R^2C+\omega^2 CL^2}{L} =1 $$

$$\frac{R^2C}{L}+\omega^2 LC =1 $$

$$\omega^2 LC = 1 - \frac{R^2C}{L} $$

I bet you can take it form here