I am wondering what we should be required to keep for declined deposit accounts. Currently, the CSR is giving the customer some type of notice from chex systems. We are not keeping anything on file at the bank to show any of these declined deposits. Should we be?

There is no retention requirements for declined deposit accounts, except if they were declined for CIP reasons the examination questionnaire will ask the bank for a listing of those accounts.

Would the notice provided by chexsystems be sufficient if denying a consumer atm card based on the information obtained from chexsystems?

I don't recall the FCRA, which is what you are complying with here, having a retention requirement at all.

If we decline an account because a customer was not approved through Telecheck, do we have to provide an adverse action notice?

Yes - you owe them a FCRA adverse action notice.