Re: dt65 Suzuki does not want to push in forward
Great that you solved the shifting mystery, you might want to mention that to the service manager or find another shop. Next priority is the cooling issue since it sounds like things got worse when you replaced the impeller, are you confident that you got all the rubber "fins" compressed and rotated in the proper direction on assembly? Was the rubber grommet at the end of the water tube in good shape? May well be just a clogged pisser but to be safe, get the cooling issue resolved first.
Next the timing, can't know for sure what model/year you have yet but if you have the adjustable idle speed switch I'm guessing late 80's. If that switch is bad, open, it will retard your idle timing, possibly causing your current stalling problem.
Lastly the prop, that cotter pin is meant to keep a castellated nut from loosening, along with spacer/washers to locate the prop on the shaft. Post some photos of what you have.