Digital Frequency Measurement
... it counts the number of pulses at the output of the shift-register

No, it uses the shift register U2 to read out the binary value captured in U1 in serial format. That count, divided by the gate period, gives the frequency at the output of U3.

Q3 (not Q2) is basically being used to detect whether the output of U3 is toggling at all, indicating that there is sufficient signal at its input. C2 and R9 on its input function as a high-pass filter, and C3 and R6 on its collector function as a low-pass filter. If there is a signal, the MCU pin will be pulled low.

1 mH seems high for the frequency range you're looking at — the series reactance will seriously limit the current available to U3. Is that the real value, or is it just a placeholder?
In any case, it is probably not necessary to have different coils for different frequencies in the ranges you're looking at, unless the sensitivity is insufficient for your needs. You'll have to experiment to see.