Wow, some mess you have going here.
I take it you bought the 2013 Skyhawk 'box of parts' kit from gasbike?
If not then some of the below is not relevant.
Not the best choice for a complete rookie but that's OK, we'll fix you up.
First off the new 2013 magneto's don't have a white wire, it is a new coil winding and the ground connects with a bottom tab and grounded to where to where old white wire used to be.
All you had to do was mount it with the blue wire up.
Telling you to pull the nut of the shaft and dick with timing was really REALLY bad advice for a brand new motor, all you had to do was mount the Mag with the 4 bolts.
The CDI is mindless, 2 wires, but you have to
remove the brass cap on the top of the spark plug!
If you broke your cap forcing over the brass nub no problem, the kit comes with a spare, just cut off like 1/4" from the end of spark plug wire and screw it in.
I have build over 50 2-stroke bikes with Skyhawk engines including 2 new ones with the 'parts in a box' as they are all I'll use and in all of those only one had an electrical fault, the ground tab from the mag wasn't soldered to the mount base well and a quick re-solder fixed that so it's not junk parts.
Undo whatever you did with the magnet and put it back tight the way it was from the factory.
Make sure your mag is mounted with the blue wire up and the same clearance all the way around the magnet.
Make sure you haven't broke the little U spring in your plug cap and take the plugs brass top off.
Then to make sure Ohm between the black wire on the mag to your head, it should be a dead short, if not you'll never get a spark because the head is the plugs ground.
That should fix your electrical issue as it really is simple.
You also mention you broke rings once, put in a new set and now your motor won't turn fairly free with no plug and the clutch out pedaling making the piston go up and down?
This is the main reason 'parts in a box' is not ideal for a rookie first build, you have to attach the piston and bearing to the crank arm and it has to be right.
There is an arrow on the top of the piston on the edge that points to the middle of the piston, actually what it pointing to is the front of the motor. Why they didn't put it on the other side of the piston pointing away from the center is beyond me but the arrow goes to the back side and points to the front (exhaust port).
There are 2 groves in the piston and they each have a little nubs that are located on the back side (intake) where the funky arrow is about 3 degrees to each side of it, one ring off to one side, the other ring off to the other side.
These nubs are where you line up the grooves in the rings to keep them in place and fill the slight void, if you forced the piston in and both rings notches were not split at the nubs they are pushing the ring out where the nub is.
In short if you can't pedal the bike around with the spark plug out pretty easy as the piston goes up and down you don't have the piston in right (assuming the rest of your drive train is good).
I'd start with the piston first and though this may sound like a condescending post to you it's more to all the people with no clue what 'Parts in a box' kit you have telling you try all kinds stupid unrelated stuff to try making matters worse.
I truly hope this gets you fixed up and others can learn something because getting a new 2013 YanDung factory engine delivered for $136 with the out of the box opportunity to check everything and do the top end right is really a great way all the way around to get around the EPA and get a nice engine kit, it's just not for rookies without proper tools like a torque wrench and metric tools to try first is all.