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Helloo does anyone know how to explain what each parts are for like the capacitors/resistors? And is there any theoretical equations present to possibly solve the values?
It's just a simple two stage opamp amplifier, using non-inverting configuration - then rather crudely capacitor coupled to a PNP transistor to flash an LED.
As alec_t posted, any of the countless opamp sites on the internet would explain it all.
The circuit shown will not produce a visible blink from the LED for a short duration BANG or POP.
Then it needs a simple additional peak detector circuit to stretch the duration of those short durations. The amplitude will still be the same.
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