Banks may check a prospective customer's credit when they apply for a savings or checking account. BBVA checks credit during checking account origination. Having a lower credit score won’t necessarily mean you are unable to open an account, it just might impact which accounts you can open.
For example, at BBVA, we offer a suite of Second Chance Banking accounts, including Easy Checking for individuals trying to rebuild their credit. If you do not qualify for the original account you were applying for, we can typically offer you another option, such as a BBVA Easy Checking Account.
Probably not. When you try to open a checking account, banks will usually do a "soft pull", meaning they check your credit, but it does not affect your credit score.
Some banks may do a “hard pull”. But they usually only do this when you are requesting credit or a loan.