To freeze or attach an account the creditor needs a court order or your permission. The question about a new account at the old bank is common because most garnishments use the language "any and all accounts held" and then they list your name if they get a court order they may attach the new account. You will need to consult with a lawyer locally.
Start keeping a detailed log of all calls and letters. You should also demand in writing all communications from creditors is in writing.
Do not give them any personal information because that is how collectors decide on which accounts to recommend suing.
If you are going to make payments use money orders and not personal checks or “check by phone” because if they find a bank account the collector will be more likely recommend a lawsuit the their legal department. Get written confirmation of any payment plan the agency will accept.
I do not practice in your state and you will need to consult with a local lawyer for protection under your state law.
I have pasted a link to the FDPCA to help you with your federal rights;