Yes most times because the coil is grounded but it needs it own ground. You say new cables, the frame needs to be grounded to the battery and the engine needs to be grounded to the frame. is that what ya got?
Would need a timing light, since your Dad messed around with the flywheel I would start there. Pull the flywheel off and see if the key is on the shaft and if it lines up with the keyway on the flywheel. If it does the timing is going to be right as there is no adjustment for it.
Make sure the pulser coil is tight also
Yes, pull the plastic fan shroud and unbolt the fan. then remove the nut that holds the flywheel on, will need to pull the flywheel with 3 jaw puller. tighten the puller up and then give the bolt on the puller a wack with a hammer and it will pop off.
I ran across an ezgo that the crank gear locating mark was wrong. You line the key way up in line with mark on engine and the cam gear mark with notch in rear cover.
Yep, that gear is only pressed on with no locating key. that's why i told him to line up the marks @ TDC and see where it all lands, said he did so if that gear had moved it would not be on TDC.
As far as I know if you remove the rocker cover and look at the cam lobe positions, the valves that are on the rock, ie one just closing and the other about to open, the other piston/cylinder is on the compression stroke.