It'll be one thing then another with an engine that has been sitting. Knock them off as you find them - whack a mole style.
Per your video, your top carb is barfing fuel because the needle is stuck open. Might be a fragment of crud from a crumbling fuel line. You should replace ALL the rubber hoses under the motor cover, and put a filter between the tank and motor in case there's any crud there. Use fuel line rated SAE 30R9 to prevent any issues with ethanol fuels.
Also, have you looked at the water pump impeller? 10 years is a long time for one even if it was new just before last use.