What is the ruling on taking a loan from a bank that buys non-usurious investment shares in the client's name, then authorizes him to sell them and deliver the amount to him, knowing that the bank determines the installment amount and profit before the procedures begin? And what is the optimal method for loans?

The transaction mentioned is a Murabaha sale to a party who promises to purchase, which is permissible if the Shariah controls are observed. Among these controls is that the bank must own the shares and they must be under its guarantee before selling them to you. It does not matter if they are not registered in the bank's name. As for your authorization of the bank to sell the shares, there is no harm in it if it is not obligatory. It is preferable, however, that you undertake the sale yourself or appoint someone other than the bank.