Is the aforementioned scenario for Forex trading—free of overnight fees and usurious interest, with payments made instantly and electronically in US dollars—considered the legitimate "possession" (qabd shar'i) required by fatwas for the validity of the transaction?

It is permissible to buy and sell currencies if the exchange takes place in the same sitting and the transaction is free of leverage, bearing in mind that different currencies are treated like gold and silver in requiring hand-to-hand exchange. Depositing into a bank account, receiving a certified check, or a transfer slip is considered constructive possession. So, if the money enters your account on the platform and you can dispose of it immediately, the required exchange has occurred. As for transferring money to the broker, there is no harm in it, as he is your agent.