From the backfiring I take it that there is one cause which might be a leaking needle valve. Make sure that the little spring damper inside the needle moves freely as otherwise the needle might leak only when the bike is running / vibrating. The backfiring is usually caused by the engine running too rich when you close the throttle and the bike is "pushing".
You can cut out the float position as this would have caused problems from word go. Leaves a faulty or sticking float needle valve or just dirt in your carb for a cause.
Ignition problems on CDI bikes are extremely rare. Sometimes they just die. (Popped capacitor) Very rarely they have temperature related problems with broken soldering on the circuit board.
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