Slide rubber boot back to expose the metal connecter.-----Turn key to on.----Touch metal connecter to ground.----Horn should sound.----And no need to open throttle to do a compression test on that simple motor.
???-----Some love to argue.-----If (a big if ) the oil seals are original they need to be replaced.----These gearcases are not robust.-----Parts are expensive if available !-----Good used gearcases are at a premium.
That lever is for manual operation of the choke.----Used when you need to start the motor with a dead battery.-----These plates close when operating the electric choke switch.-----Time to get an owners manual or get someone to teach you about this motor.----You do not want to be educated through...
Judging by statements so far , you need a proper manual in order to understand how these fine / smooth running motors are put together.----There are no short cuts.----Mistakes will be expensive.
Just an example of plastic parts failing with time.-----Should not be hard to find a used one.----But new might be a better option.----Then again a new one may have been made 15 years ago.----Doubt there is a roll pin needed to stop the pinion.
The trouble shooting starts with a compression test.----Post the actual values here.----Next is a spark check.----Do you have spark that jumps gap of at least 3/8" on all leads?----The surging points to a fuel supply issue.
It should slide right off.-----In salty water the prop should be removed about once a year to grease the splines.-----Try a hammer and a block of wood.
Simple job to replace the o-ring in there.-----But I have seen this presenter trying to hammer tapered dowel out of V-4 and a V-6 block.----Trying to POUND them out in the wrong direction.