The correct starting technique is shown here:
The function of the compression release is to release compression while setting up to start by allowing you to advance the engine through the first part of the compression stroke without resistance. It does this by raising the right hand exhaust valve off its seat slightly.
The hot start plunger opens an air passage from the intake bell in front of the carb slide to the intake tract on the engine side, basically creating an air leak of a controlled size. When the engine is very warm, as when it was stalled while running, it is exceptionally prone to refusing to start for reason of being too rich. The hot start helps with that. It's not usually needed in cases where the engine has just a minute or two to cool down.
Fuel leaking from the carb is usually a problem with the float/level controls. Either the float is physically stuck (or assembled upside down), there is dirt between the needle and its seat, the needle tip is worn or damaged, or, in your carb, the O-ring that seals the needle seat to the carb body is leaking.
When working on the carb, DO NOT remove the four screws inside the top of the float chamber holding the upper and lower body halves together. No gasket is available for it. Also, do not remove the throttle position sensor unless you want to have a whole bunch of fun trying to recalibrate it.