The pilot screws are at the the front of the carbs, on the bottom centre. They are recessed so you won't actually see them. The centre one is a ***** to get to.
Missing in the damp is not normal. Mine has done some long journeys in torrential rain and never missed a beat. That probably does not help you much, but at least you know it's not normal.
The centre plug can be "entertaining". Not so bad once you get the knack. You might find it easier to use a socket & ratchet over the plug wrench.
The fan hardly ever comes on- mine has been on maybe twice in two years, once stuck in London traffic and the other time in the garage when I was balancing the carbs. I suspect running hot is not really an issue with our typical weather.
You could test the fan switch by heating it up, either in-situ with a hot air gun or by suspending it in water with an ohmeter attached. At 98c or thereabouts the switch should operate.
I doubt if you need to worry about the coolant pump- it's mechanical and very unlikely to go wrong.
I can't really help with the alternator bolt thing, other than if you are really paranoid pull the alternator and check it. It's an easy job.
