If the credit card is frozen, will the bank inform you by SMS?

Not necessarily. It depends on the bank.

Fill in the form when you apply for a card. There are instructions for using the rules on the back.

One of them is: (I only remember this incident)

When the bank foresees the use risk of the customer's card, it can unilaterally suspend or freeze the card without notifying the customer.

If the card is in arrears. The bank can call.