Adjust the neutral before you worry about the carb adjustment. don't drive the bracket all the way to the top, just nudge it enough to stop the wheels from turning after you set it in "neutral" with the pedal. Don't lock the pedal down or the brakes will stop the wheels.
Go forward and back with the lever, then hit the pedal again. should stop the wheels. If not, adjust the bracket until it does. Slop in the linkage will often result in a situation where it will go in neutral from forward by hitting the pedal, but if you are going in reverse and hit the pedal, it doesn't quite make it into true neutral. Sometimes that's the best you can achieve.
Throttle "hunting" or going up and down in RPMs is usually a carb adjustment. Follow instructions in the manual, I think 2 turns open on the main jet and 2-1/2 turns on the idle jet to start. Put some load on the engine (engage the mower) and make small adjustments as described in the manual.
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