I just use a spray bottle with 2 stoke mix but starter fluid works well when sprayed into the air filter housing with the air filter element removed , some times 2 strokes won't run properly without the snorkel and filter housing installed .
I've had a 2 stroke backfire when the spark is weak ,usually a bad spark plug or coil.
It might be worth filing the points and putting them back in so you can set the timing if the coil plate is adjustable some have adjustment and some don't ,then once the motor is running fit the module.
Might be easier to remove the starter and put a socket extension in a drill then use the drill with a socket to start the mower.
It can only be one of 3 things stopping it running if you have 2 of the 3 right ,1 spark problem ,2 fuel problem ,3 mechanical problem.
If the crankcase seals are leaking it will be hard to start.
