Sorry, i don't do sketches or schematics.
But two strokes can just exhaust. Piston goes down, exhaust port opens, exhaust goes out.
But it is possible to.put an expansion chamber on the exhaust. As the exhaust pulse goes out, it expands in the chamber causing negative pressure behind it, which sucks out the exhaust on the next cycle. Works great at a specific RPM, works ok for a small range of speeds.
I don't know of two ignition systems for motors, and why it would be different depending on the number of wheels. My motorbike works exactly like my car.