Are savings and investment accounts in a bank that claims to be Islamic and are based on a Mudarabah contract, compliant with Islamic Sharia, according to the terms and benefits mentioned for each?

No Shari'ah prohibition appears in the two types of investment mentioned with the bank, as long as the bank invests the funds through means compatible with Islamic Shari'ah, does not guarantee the capital, and both parties share the profit — if any — at a known ratio at the time of the contract. If this is achieved, then there is no harm in investing the funds and taking the profits, especially if the bank has a Shari'ah supervisory board.