ZCD is a hardware function, it produces an electrical signal that is read in by your PIC so it knows the state of the AC line.
I am greatly concerned by the wording in your schematic "LINE" and "NEUTRAL", if these are the AC power lines you should expect considerable smoke, anything more than about 25V RMS at the input will damage the regulator and surrounding components. Also be aware that if it is working from the AC power lines, it has no isolation and therefore presents a lethal risk of electric shock unless the whole thing is entirely enclosed in an insulating box.
How it works is simple, the two bridge rectifiers (which you can simplify down to one) convert the AC to DC. BR1 is then used to maintain charge across C6/C7 to provide power for the regulator. BR2 has no filter capacitor so the voltage at it's output drops to zero as the AC passes transits between positive and negative polarities. When the voltage is above about 0.7V, it lets current flow through R1 to make Q1 conduct. The idea is that Q1 conducts all the time except when the voltage from BR2 is below 0.7V so it produces a pulse output around the zero voltage crossing point.
I think it would be advisable to add another resistor of about 330K between the base of Q1 and it's emitter to be certain it turns off adequately, otherwise residual charge might leave it conducting longer than wanted.
Brian.