your oil will usually start to turn black at around 1000-1500miles of normal driving. if u beat the shit out of your car its obviously gonna be quicker. also large amount of blow by can cause this too.

i dont see what a water leak would have to do with anything, internal or external. an increase in coolant temp will increase your oil temp a little but unless youre running your car overheating then it wont have that much of a direct effect on your oil and youd have a lot worse of problems than dark oil.