1. Certificates of Deposit don't require a signature card, at least for FDIC insurance. Some banks use a forms setup that may have one or something that is similar and others use a master agreement. Depending on the forms your bank uses, you may have to discuss the documents CDARS offers if your bank was to join that network.
2. & 3. Your questions are best posed to teh CDARS group. https://www.cdars.com/ Theses deposits are essentially a way for one bank to manage a depositors funds in a way such as to preserve the relationship and maintain full FDIC coverage by placing these deposits at other CDARS participating banks. It may be that when your bank places deposits elsewhere, it then receives deposits as well so there is no net loss in deposits. These are essentially brokering relationships. It is not a way to skirt BSA laws or obtain some form of Swiss bank confidentiality. The depositor would still have to be known to the bank and it have to be comfortable with the relationship.