The governor bolt was stripped because it has left-handed thread. The person who tried to loosen it turned it the wrong way. Very common error.
The governor's ball guide is likely damaged, which is why the RPMs are creeping. Two pins on the back of the guide keep the guide at the same speed as...
Absolutely sure. This unneeded element is inside the crankcase. Its purpose was to help separate air and oil droplets, keeping the oil in the engine while letting the air out of the crankcase. Has nothing to do with the engines outside environment.
Can a coil fail? Sure. It is common for both coils to fail, not likely. That is why I suggested removing the ground wire from both coils to see if either has spark.
The coils are best tested for spark while on the engine. You can use a running (lightbulb) spark tester easily to see if the coils are doing anything. A gap-type tester (pictured) is best for loading the coil. The SE line is for "small engine" or about 1/4" gap. Don't hook the ground wire to the...
The black oil may be temporarily ok as long as the oil level is not over full. You may smell fuel out the exhaust as at operating temp, some of those hydrocarbons will burn off.
The only thing I do know about aftermarket carburetors is that usually they don't work well. What is the problem with the original carburetor? The Nikki carburetor has transition ports that provide enough fuel during the transition from low to high idle. Maybe the aftermarket carburetor does not...
So at high idle under load is sounds good? WOT on a governed engine is when the engine is under heavy load and losing RPM. If the engine runs fine with the PTO engaged, then the idle jet likely is incorrect for this engine or debris in the idle circuit. The engine has no purpose at mid-throttle...