If you go off half-cocked, you take a rash action without being prepared for the consequences. It refers to an old fashioned single action revolver, which had a half-cock position in the action where it would supposedly not fire. If you made a mistake and it was at full cock, you would fire prematurely, possibly with devastating results.
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.