Is it permissible to sell used gold and have its price determined by the goldsmith, then buy new gold from him for an equal or different value? Is this considered permissible (halal) or usury (riba)?

There is no harm in exchanging used gold for other gold if they are equal in weight and the exchange takes place in the same session, or by first selling the used gold and receiving its price, then buying other gold with that price. As for exchanging gold for gold while paying the difference between them, it is not permissible and is considered Riba al-Fadl (usury of excess).