1. Distilled Water was used in the coolant system with no anti freeze for the "first" first start and go kart. Should I drain all the coolant now and refill with the appropriate coolant anti freeze mix? (BTW no coolant leaks over the last 2 years);
2. Gas ... there is a about 1/4 of a tank ... should I drain and refill with fresh gas?
3. Oil ... original oil in the engine with no leaks over the last two years ... can I still use it as is?
#1 - Drain out the plain water, maybe flush the system to get any crud out that may have broken loose. Fill with 50/50 premix and go with it.
#2 - YES. Today's gas is crap. Drain the tank into a few cans and run it through the lawnmower. I wouldn't "refill" it, maybe 5 or so gallons (in case there's a problem... you know Mr. Murphy? He'll show up with a tank problem as soon as it's filled.)
#3 - Spin on a new filter, top off the oil and run it. Your original go-kart run would've trapped whatever crud was in the system. Consider an oil change after the first 1000 miles.