What you have is one of the early engines. Wood tone handle instead of black, early coil, the blower housing screws are from the back instead of the heads on the front, no primer carb, jet screw on the side instead of the top, etc etc.
All of those are normal things for an early type engine.
There should be a hole in the bump on the top of the blower housing which holds a metal tab to ground the spark plug off to stop it.
I'm not sure what you mean by it having a "single point". The points are under the flywheel and under that little cover that will be exposed after the flywheel is off. There are 2 point contacts that touch one another and probably need to be cleaned because they oxidize over time and that will prevent continuity because they aren't actually touching together.
You can mix modern 2 stroke oil at 32:1
If the diaphragm in the carb is stiff it will need to be replaced in order for it to pump fuel.