I can't answer all the questions, but...
3. There are 3 positions on the tap - On, Reserve and Prime. Because your Blade has a tap that opens when there's a vacuum on the engine end, when it runs out of fuel you need to prime the carbs. Prime on the tap bypasses the vacuum switch and allows fuel to flow to the carbs regardless.
If you could post pictures of the other bits then I'm sure I can help. I suspect the random plastic twiddly bit is the idle speed adjuster, though.
Have you tried phoning (or visiting) a Honda dealer to see if they can give you some advice? Probably not because you've not had the time since discovering the problem (duh) but it might be worth a try...
SB