Key is a "Woodruff" available at any small gas engine shop,
most automotive shops and some hardware stores.
Same as used on a lot of small gas engines. About $0.60 each.
Take your flywheel or the pieces and they will find you the size.
Looks minor to me. Meter the coils or check for broken wires.
Coat them with a bit of epoxy if they are bare or loose.
Clean up the taper like you were told and you'll be riding after supper!
Check the crank.
When straight up (TDC) check carefully for up and down play.
If you feel any, even a tiny bit, you will need a crank. No exceptions.
Piston looks reusable if you are not too fussy and you don't find any cracks
on the skirt, but a new one is always a good idea with a 2 stroke.
If you do think about a new piston, check the bore out first.
If there is any ring ridge you might want to bore or hone it over size.
This job can be as simple or as complicated as you want it to be!
Good luck and happy trails!