not sure on problem 1 or 3 but as for number 2....
I used to work in the bike industry, and that sort of fault usually meant that it was running rich. As it is already running, there is enough spark/compression/unburnt fuel to make it continue running, but on shut off it might be over-fuelling. We used to get it even on stock std bikes, just needed a re-flash of the ecu and it was right as rain. Cars are probably different tho, I haven't had enough experience with car engines.
VZ Calais + 690 KTM = Happiest bloke on earth.