Does the wish bird spell work on wishes that are impossible without the aid of magic and if so how long does it usually take to come true?

No. If something is impossible "without the aid of magic" then it is simply impossible, as there is no such thing as magic. Spells do not work. You cannot get something simply by wishing for it. Sure, sometimes things happen by chance, but the best way to get something is not by wishing, but by doing.