No I haven't tried the circuit.
Yes, the MOSFET needs to be off to allow some of the power to be taken from the lamp to power the control circuit. The zero crossing is required so the MOSFET only turns on/off when the mains voltage is near zero. Obviously, the MOSFET needs to be off for long enough to allow C1 and C2 to charge.
There's no way to do this without a neutral, other than to take some power from the load to power the control circuit or use another power source such as solar power or a battery.