how does this circuit works
Could this be a clap-switch, you clap and the light toggles ?

Mk1 and R1: Indeed microphone to ground and R1 to supply is more usual but that does not mean this does not work. For the microphone it does not matter, it just needs a biasing voltage, which is has. And it will modulate that biasing current with the incoming audio.

C3 looks to me like a low-pass filter in combination with R4

Yes R7 and C4 are supply filtering for the microphone amplifier. C4 is large but it just depends on what suppression you want at certain low frequencies. 10 uF or 47 uF, it will not make much difference.

The right side is indeed somethink "multi" but there are no capacitors inside the circuit itself. C5 and C6 only couple the microphone amplifier to this circuit. C5 and C6 are not part of the circuit itself. So it's not multivibrator.

It's a flip-flop, it has two states: Q3 conducts and Q4 does not or the reverse: Q4 conducts and Q3 does not. When Q4 conducts the LED lights up.
Switching between the two states is done through C5 and C6. If the line to the microphone amplifier is pulled low, the flip-flop changes state.