Is it permissible to sell to children, especially given the frequency with which this occurs in stores?

If the child is not discerning, then his buying and selling are void (batil), but his disposal of a minor item is permissible. As for the discerning child (al-sabiyy al-mumayyiz), his disposal of a minor item is valid. However, regarding a significant item, there is a difference of opinion among the jurists. The preponderant view is that it is permissible with the permission of his guardian or if his guardian ratifies his disposal. This is the view of the Malikis, the Hanafis, and the relied-upon position (al-madhhab) among the Hanbalis. In contrast, the Shafi'is and, in one narration, the Hanbalis, held that his disposal is not valid.