Yes it is normal for the fan to come on, esp. for short trips when the engine is actually hotter because very little air is coming across the radiator...Unless you are very familiar with drive chains, I would have that checked by a service department. But yeah you will have some slack when bike is sitting, you donĀ“t want it too tight or too loose. My 06 ZZR the the standard slack is 1.2-1.4\