I wouldn't worry about the synchronism, that's controlled by the lobes on the camshaft and they don't change.
the firing order is 142536. thats left-right left-right left-right going from front to back. various valve cycles do overlap.
the cam is driven at the front by the chain, the rear of the cam drives the oil pump & cam sync so if it were somehow broken you would have no oil pressure.
the ticking is something that is out of place or broken, there is a gap that slams shut as parts cycle. or something moves in a way it shouldn't.
crank the engine slowly by hand, feel for any catches or whatever. rig up a piece of wire pointing at the harmonic balancer so you can note where in the revolution
anything occurs. does it repeat? plugs out, you want it easy to turn over.
is compression on 3 still zero? are you sure it's actually zero, not 4 or 8 or15 or whatever? loosen both rocker arms and try it again with finger & hand cranking.
if yes, ignoring all the other cylinders start cranking the engine by hand and watch the # 3 valves.
the sequence will be about 1 full crank turn with both valves closed, ( compression + power ) then the exhaust opens.
just as the exhaust is almost closed the intake starts to open. after the intake does it's thing it's back to 1 rev and nothing.
you can rock it back "n forth to get a good look if needed. inspect and rattle stuff.
rig up another wire to measure how far each valve opens. the resting height may be slightly off but the motion should be very equal. that checks for a collapsed lifter.
we're assuming the lifter is in correctly, and the guides are ok.
remove pushrod, check if it's bent, or clogged. oil passes thru them to the rocker.
side note, hydraulic lifters work in a state of compromise between the oil filling them up and the valve spring pressure squeezing the oil out.
the allowable lash is huge, must be at least .050/one turn but not bottomed out. the innerds of the lifter are quite happy anywhere in the middle.
functioning properly the lift is always the same no matter where the lash is set at.
my 2 cents worth, but remember they don't make pennies anymore.
