The weld didn't penetrate, so that's why it cracked again. Who ever did it was a novice welder and was welding too cold and fast. You can tell by the lack of a bead pattern (along with that horrible splatter) that they either didn't know how to weld properly, or care too much. Make sure your weld penetrates properly and it will be good as new.
And yes, all of the galvanization was burned off in the first repair, so no worries about that. Even if it hadn't, the amount of zinc you'd be exposed to in that small of an area would not make you sick. If you did it a lot, then you'd want to take precautions. But this isn't that. Usually I would always suggest erring on the side of caution, but honestly - the zinc thing is so misunderstood. Zinc bonds with oxygen to form a gaseous zinc oxide fume. Zinc Oxide is non-toxic - its used in diaper rash treatment for pete's sake! The fumes, in abundance, can give symptoms similar to the flu, but they pass. I've welded galvanized metal a good bit, and I've had zinc flu. It sucks, but its not deadly.