Can my ex-husband open a checking account in my name without my permission and signatures?

There are more facts needed to ascertain what you should do. Generally speaking, he cannot open an account in your name that binds you but you must first ascertain what the settlement agreement or divorce decree specifies. YOu used "agreement" in quotes which suggests you are referring to how you have been handling the matter but that this method has not been reduced to writing and approved by the court. If the original agreement specifies that it can only be modified in writing (and they typically do), then he may still be operating under the original agreement. You probably need to take your original settlement agreement to counsel of your choosing and get them to review the specific language to determine what you need to do.

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Neither of you can agree to ignore the judge's order as to how payments are made, and since none of us here have read that, none of us can answer you. I'd suggest calling the attorney who represented you to determine what was required and what is appropriate.