Do closure properties for languages go the other way? For example I know the union of 2 either decidable or recognizable languages is decidable or recognizable. But say the union of two languages is decidable, does this tell us anything about themselves?
No, it doesn't tell us much. Intuitively, union erases information; it's not normally a reversible operation.

So, for example, the union of a language with its complement is clearly decidable and recognizable, regardless of any category in which the language might or might not belong.