What is the ruling on depositing money in banks, especially if Islamic banks invest their money in conventional banks and stock brokerage firms, and what is the harm if banks trade on my behalf if I am unable to trade myself?

Usurious commercial banks deal only in debts. They borrow with interest and lend with higher interest. Calling their borrowing 'depositing' does not change its reality. As for Islamic banks, they rely on investment methods that have jurisprudential rulings approved by jurists and jurisprudential councils, such as Murabaha and parallel Istisna'. However, it is not permissible to invest in Islamic banks if they invest their funds in usurious banks or stock markets that violate Islamic law.