Filters in IR alarm circuit
Q2/Q3 is a Darlington pair configuration (not Q5/Q1).

C3 is a DC-blocking capacitor, so that only the signal goes into Q2 and not the DC bias given by D1/R10.

R14 provides DC bias for Q5, and C11 will short circuit R14 for AC signals, giving a high AC gain for Q5.

C2 is a bootstrap capacitor, providing a higher input impedance at Q2.

Now think of Q2/Q3/Q5/Q1 as a high gain amplifier (like an opamp).

From the output you have a (frequency-dependent) voltage divisor given by R5/C5 and R11/C7. The signal in the midpoint is used as feedback to the amplifier by means of R6.

You can do the math for this voltage divider; I suspect that the overall circuit is a band-pass amplifier.