probably not, unless you live somewhere where it's hot.

I think they'll be just fine, as long as you keep it under 2-3 days (not due to your frosting going bad, but due to things beginning to dry out past that point).

probably about 24 hours between frosting and eating? should i refrigerate them over night?

I think not, but it could depend upon how long it is between frosting and consuming.

Probably not. Generally there is enough sugar in the frosting to make it hygroscopic which prohibits bacterial growth. Eventually they would mold, but the should be eaten well before then!