Closing credit cards can affect your credit score because your credit line will decrease from the loss of cards, so your utilization ratio (balance / credit line) will increase. The usual advice is to try to consolidate your credit line before closing, but that might be harder when switching providers. Still, you can easily reduce the utilization by just paying the balance. So closing accounts does not have too much of a negative affect on your credit score. (My understanding is it does not affect age of accounts, because closed accounts continue to "age." Not sure about that though.)

Your bank account is not a line of credit. So it does not affect your credit score. It does affect score on another system called ChexSystems.

Yeah that was why I left the cards open but at this point I don't care. Getting out of BoA.