I will answer your questions in the order that you asked them.
1) C2 is a DC blocking capacitor so that Q1 can be biased OFF by a weak current from R2, a 1M resistor. Sufficient sound levels will bias Q1 into an OFF state, but without sound C2 discharges and soon R2 switches Q1 ON again. If Q2 is OFF, Q1 turns on during AC cycles but is OFF when AC crosses zero volts and Q1 is ON.
2) The red LED is a voltage regulator and indicator as well. R4 limits the current to about 3mA peak. The LED clamps the voltage to less than 2 volts and C1 removes any AC ripple so the circuit has a clean 2 vdc to work with. The LED goes out if the circuit is triggered by sound due to Q2 being ON and reducing the voltage across it to near zero. This means no power for the mic circuit either, so eventually C2 discharges and Q1 is ON, turning OFF Q2 and the LED comes back on, and the circuit is ready to be triggered by sound again.
3) Yes, without the LED there is no limit to the voltage and it could rise to 300vdc or more. It is debatable whether C1, Q1 or the mic shorts out first. There is not enough current to make things go 'BANG' but crucial parts would be destroyed without the LED.
4) This circuit is for AC only because Q2 needs that zero crossing of the AC voltage to turn off after C2 has timed out and Q1 is ON again. Simple but effective circuit.