A spell can mean a fairly or relatively short period of time; you'll hear weather forecasts predict a dry spell. Sports commentators will say that a sportsperson is going through a good spell when they're performing consistently better than they normally do.
If you have a crack at something, you try to do it. If someone is attempting to do something and they are unsuccessful, you might say, "Let me have a crack at it" suggesting that you might be successful at performing the task. ('Take a crack' is also used.)