OK, so you have two distinct problems. One is electric start, and the other is stalling.
A number of things could cause the failure to electric start. You cannot start in gear, for example. Likewise, if the starter solenoid is not engaging, 12v will not go to the starter motor. If the 20a fuse is blown, the solenoid will not engage. If you are properly grounded, and you apply 12v to the starter, it should turn. If not, there may be an issue in the starter motor.
For the motor to slow down and stop, that is usually fuel starvation. If you have a bad o-ring in the primer hose (or it's not seated correctly), air can get drawn into the fuel system and cause stalling. So can a closed tank vent. When it stalls, you can open the drain on the side of the carb (uses an 8 mm socket) about a half turn and see if a few ounces of fuel comes out. If only a drop or two, the carb is dry.