What is the ruling on depositing money in savings accounts with Islamic dealings in commercial banks, and what is the ruling on the interest generated from them, knowing that they belong to a regular commercial bank?

It is permissible to open a savings account in an Islamic branch of a usurious bank, provided that the Islamic branch operates independently from the usurious main institution in its transactions and adheres to Sharia-compliant dealings. Otherwise, engaging in transactions with it is forbidden.