Is it permissible to back doubtful debts, whose collection is uncertain, with returns that are contrary to Sharia, and is this action correct, and what should we do with the profits that were distributed to us?

A bank is not considered Islamic unless it regulates its transactions and investments according to Shariah principles. This includes its relationship with the Central Bank. It should not deposit funds with the Central Bank for interest unless absolutely necessary. In such cases, the interest must be disposed of by spending it on general Muslim welfare and not used by the bank to pay off its debts, as the bank is not indigent. Dealing with this bank is permissible for its legitimate transactions. Any profits you receive from Mudarabah deposits are permissible, but you must ensure that the bank does not revert to usurious practices; otherwise, you must withdraw your funds and sell your shares.