There is a circuit error. Diodes D1, D2 and D4 will provide more current through the electrodes than taken by the circuit so the current through the electrodes will not be symmetrical AC as you want. To prevent DC through the electrodes put a non-polarized capacitor in series with the electrodes. For that you wouldn't need D2 and D4, just D1.
You can put the LED and its current limiting resistor in series with whatever you have for DC power at the right of the schematic and the collector of Q3. The value of the LED resistor depends upon the DC power voltage and the desired LED current.