R2, R3 and C3 form a giver triger circuit beginning at the reset IC 555 for 2 seconds. If you want to use a series of Simple PWM controller 555 with the V + not +12 V, it does not matter to raise tilapia R2 where (V + * R2) / (R2 + R3) is about 2, because it limits the signal level reset is 0.5 .. 1V. If you do not do that, then signal the kickstart to get too close to the limit reset signal reception.
Q output of 555 on the Simple PWM controller circuit 555 is used for driver PWM pulse, so that the discharge pin is used for transistor output driver instead. This is an open collector output, and is used as an active signal is low, so it can work. D3 protects the output transistor of the load induction. You may replace any suitable transistors for Q1, BD140 is 1.5 amps.
C4 and C5 is the power decoupling capacitor for the IC 555 on the Simple PWM controller circuit 555, which produce relatively large level of push-pull output stage.