The "mixture screw" controls the amount of air entering the pilot (idle) fuel circuit, while the amount of fuel is determined by the size of the pilot jet. Turning the screw counterclockwise allows more air into the pilot circuit, thereby leaning-out the mixture. Those are the basics.
In actual operation, it's a dynamic system...affected by throttle position and vacuum. Once the throttle is opened past a certain point, ~1/8-1/4, the pilot circuit becomes inconsequential...the main circuit takes over. Below 1/8 throttle, the pilot circuit takes over. The smaller the throttle opening, the higher the vacuum inside the intake. At high rpm, the engine is displacing at lot more air volume per unit of time, unless restricted by the throttle. What's not been mentioned is the fact that closing the throttle at high rpm runs the vacuum level sky-high, increasing the air & fuel flow through the pilot circuit...until rpm drops down closer to normal idle level. A carburetor works on pressure differential...i.e. it needs vacuum to flow fuel. Abnormally high vacuum can draw excessive amounts of fuel through the pilot circuit, a phenomenon known as "pullover effect".
So, what causes the popping exhaust? The answer is the combination of just the right air:fuel ratio and an ignition source. Below about 3% concentration, there's not enough unburnt hydrocarbon to ignite. About about 15-20% the mixture is too rich to ignite. Under high-rpm/closed-throttle deceleration there's typically static high-vacuum on the intake side and dynamic/resonant vacuum on the exhaust. Unburnt fuel accumulates inside the exhaust. If enough atmospheric O2 enters the hot exhaust stream, the mixture goes "bang!" each time it reaches the sweet spot. Since the pilot circuit can't flow enough fuel to turn the muffler into a steady-state afterburner, the explosions are cyclical, though they seem almost random/erratic.
With all due respect, you may still have a pinhole leak somewhere in your exhaust. Just having a slightly loose nut at the port flange will usually be enough to cause this...even on a perfectly dialed-in engine/carb combo. Ask me how I know. That doesn't mean that excessive blowby, oil control problems or carb adjustments have no effect, they're just more likely to be secondary...if present. If the piston rings aren't sealing properly, then it's highly likely that glowing-hot carbon embers are the ignition source for the unwanted popping.