(B) How the heck does the windshield washer activate?
As you have found out, there is a rubber bellows inside the foot pedal. One light push, and a "normally open" switch closes, and the wipers function. Great for when a passing semi sprays your windshield with muddy water! A harder push, and you compress the bellows, which theoretically squirts washer fluid on the windshield. But often the bellows (or more accurately, the hose connection on the bellows) deteriorates, and the rubber cracks. Then no more washer. Or, the check valve in the washer tubing fails. That can be easily fixed. The solution to a broken bellows is to simply buy an aftermarket washer pump, and either rig up a dash switch, or better still, install a push switch in place of the bellows. That's what I did with mine.
(C) I've got cold start problems which indicates the auto choke ain't happy. Can that portion of the carb be disassembled, cleaned and reassembled without removing the whole carb (it's the stock Weber)?
Well, the stock carb is a Solex, so if you have a Weber, you have half the battle won. If you have a water activated choke (which the Solex does have, as does the DGAV model of the Weber), it can usually be adjusted to function properly without disassembling the carb. So can the electric choke version of the Weber (DGEV). The choke can function properly, that is. The Solex is a lost cause, and one of the most typical complaints is with cold start, and especially with "warm" (between cold and hot) driveability. They stumble and fart around like a 90 year old bus driver! (apologies in advance to any bus drivers in the group). Replace the Solex with a Weber. More can be found in the Mechanical Section, under "Fuel System"