Year of a yamaha out board

No, he didn't.
Next time Google it yourself:
https://www.politifact.com/facebook-fact-checks/statements/2019/feb/14/viral-image/no-beto-orourke-didnt-dismiss-veterans-and-elderly/

Yamaha actually lists the date of manufacture on the transom bracket or a label on the bottom

Hello,
It is not possible to retriev a year on yamaha with only the serial number.
On the serial number sticker, you'll find other data, like type, length, horsepower, weight etc...
In the link I give you'll find all the needed data and you will be able to obtain a mfg year...
Posts Tagged Yamaha Outboard Serial Numbers

Carb issue if the ignition system checks out ok. Just had this same issue with a mercury 150. One of the three carbs had a sticky needle valve.

probably a power prop not a speed prop it makes a big differance

Try this and see if it works for you. I think yours may be a CS-001.
Beto Child Seat Instructions

yamaha has changed up designs but most are under the water jacket resevoir. This will be a rectangle looking box cover with several bolts on the side.

Google "beto bicycle seat".

Amazon, eBay, various other stores...

try reconnecting the wires