Is it permissible to use rebar donated by an individual to the mosque, when it later became apparent that the donor's method of acquiring it was unlawful, or should it only be used for the restrooms, or disposed of outside the mosque?

You have not clarified how the donor acquired the forbidden materials, and the ruling differs accordingly: that which is inherently forbidden (like usurped or stolen property) must be returned to its owner. If returning it is impossible, it should be spent on general Muslim interests (such as building mosques). As for that which is forbidden due to its acquisition (like earnings from usury), it is forbidden only for its acquirer, and others are permitted to benefit from it, such as donating it to build a mosque, unless there is an opinion that considers mosques to be too sacred for ill-gotten wealth, in which case it should be spent on mosque annexes like restrooms.