All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
We will answer your question in two points:
1. Opening an account in a bank that deals with Riba (interest and/or usury): You mentioned that you are aware of the Islamic ruling in this regard, but the necessity is valued according to its proper value. The need for an account in those banks could be met by a current account and this is better than a savings account. Therefore, it is not permissible to open a savings account with the possibility of opening a current account to meet the necessity and the purpose. For more benefit, please refer to Fatwa 90054.
2. Using that card which enables you to buy with your balance in the bank: This is permissible but if it is the bank that pays the money that you get when using that card, then it is not permissible to benefit from it because this is nothing but an interest or gift from the bank in return for dealing with it by saving your money in it, i.e. you lend it money in return for an interest.
Therefore, it is not permissible to benefit from those incentives; rather, it should be spent in the same fields that ill-gotten money should be spent in. For more benefit, please refer to Fatwa 181177.
Allaah Knows best.