Is the bank required to notify me immediately if my account/debit card/credit card has been compromised (stolen / lost / used without authorization)?
No. There is no Federal law that requires the bank to provide notification. The best way to protect yourself is to review your accounts and statements regularly, and notify the bank immediately if you spot any irregularities. Some banks may monitor an account for unusual activity and notify you. However, the bank is not required to do so.