First, the shift rod....
The clevis pin retained by a cotter pin that you describe is actually inserted into a hole in the oddly shaped adjustment nut. You have the transmission in neutral and pull the cotter pin and remove the clevis pin from the shifter linkage and the oddly shaped adjustment nut with the hole at the top. You then move the adjustment nut and rod away from the shift linkage clevis just enough so that you can unscrew the nut from the shift shaft counting the turns as you do so. The nut must be removed from the top of the shift rod because it will not pass through the bottom of the oil case and extension case as you pull the gearcase, with shift rod still attached, down and away from the outboard. The adjustment nut is left off of the shift rod until you put the gearcase back on the extension case after working on the water pump. The adjustment nut is then threaded back on to the shift rod threads using the same number of turns that it took to remove it. This maintains your previous shift rod adjustment.
Now the throttle cable adjustment....
Shift lever in neutral.
Turn throttle grip to start position.
Adjust the cable so that the throttle arm contacts the shift arm by turning the nuts at the end of the cable housing.
Tighten the nuts.
Close the throttle grip fully.
Adjust the stop screw so that the carburetor throttle plate is fully closed.
Make sure that the throttle plate opens all the way when the grip is twisted to max. This should ensure your engine achieves full operating rpms. (5500 rpm)
These adjustments are made because Honda wanted to limit the rpms when the outboard is in reverse gear. (3000 rpm).
If, after performing these adjustments, the outboard doesn't get to full rpms in gear, it's possible something could be worn or damaged in the twist grip. Other factors can also limit full rpms too.
Wrong or damaged prop.
Misfiring cylinder
Engine out of time
Poor fuel quality
When the engine is cold, some outboards may start easier if the throttle is left fully closed and 1/4 to 1/2 choke is used.
When restarting a warm engine, "cracking" the throttle open slightly may prevent flooding.
If you think you have flooded the engine, opening the throttle fully and giving 3 to 4 pulls should clear it.
I hope this helps. If you still feel confused about any of it, I will be happy to try and help you get past whatever the "snag" is.
Good luck.