If you could elaborate on what specifically you mean by the points don't work, even with the new parts you got.
Mechanically are the moving opened and closed. Does the movable part of the points come off the pivot, etc.
Pictures would be best to see. I found I may have had the spring on in a different way and eventually got it right and the movable part of the points did not come off the pivot. The line up of the points round end to contact the other side of the points was off and when the spring redone different they were better.
If the points physically work right and there is a problem with hot spark I always sand paper a little on all the places I can on the mounting of the points and magneto. I add external star tooth lock washers as well. The flywheel I sand any rust off and actually use the counter weight side of the flywheel with the sand paper in it as I adjust the magneto as close as possible to the flywheel. Then while turning the flywheel I pull the sand paper out.
The testing of the magneto and the condenser I would try to find specs if there is a concern.
Aside from the values for at least the condenser (being a capacitor), I can say it should not pass direct current. Separated from the engine with an ohm-meter on the condenser it would show initially some conduction and then go to high ohm value and stay there.
Taking the leads of the ohm-meter away for a few minutes or reversing the polarity will have the same results. Initially disconnecting the leads and leaving the same polarity it should be at the same high ohm reading which also means the capacitor is holding the charge for a short while.
The primary and secondary coil of the magneto testing I found this:
http://www.ehow.com/how_12078179_troubleshoot-magneto-coils.html
The condenser testing found:
http://www.ehow.com/how_5526059_test-condenser-small-engine.html
Your leaf spring is really looking good. It must be rewarding to do things from scratch and see it all come together.
MT