Is it permissible, Islamically, to sell money granted by an Islamic company on the stock exchange at face value without any consideration or interest, and then sell it for another currency, resulting in profit or loss?

What you have mentioned regarding the brokerage firm's dealings is leverage or margin, which is a loan guaranteed by the company. It stipulates that transactions with the amount must only be conducted through it, and this brings it a benefit due to the increased commission on buying or selling. The Islamic Fiqh Academy has issued a resolution stating that the broker's stipulation to the client that his trade must be conducted through him leads to combining a loan (salf) with a compensatory contract (mu'awadah), which is equivalent to combining a loan and a sale, a practice forbidden by Sharia. Furthermore, every loan that brings a benefit is considered unlawful usury (riba). Therefore, it is not permissible to deal with it; rather, one should only deal with his own capital.