Is trading on the global currency exchange permissible or forbidden, given that the brokerage firm allows trading with amounts exceeding the deposited capital, takes a commission on trades, and transactions are executed instantly without knowledge of the buyer or seller?

We understand from the question that you are purchasing for one hundred thousand while possessing only twenty-five thousand, and this transaction is impermissible because part of it is sold on credit. For the permissibility of currency exchange (selling currencies), it is stipulated that it must not be on credit, and that the possession or its equivalent takes place in the contract session, such as the purchased currency entering the buyer's account and its price entering the seller's account immediately after the transaction is completed. It is also stipulated that other Sharia prohibitions, such as gharar (excessive uncertainty), jahalah (ambiguity), and deception, are absent.