You file a DBA because you are doing business under a ficticious name. Your LLC can file multiple DBAs. DBAs are not a business form so they don't file taxes and I don't think you can get an EIN. The bank is going to want to know the legal entity and, especially these days, will probably want a copy of an official document - not a DBA notice.
You can conduct business under the DBA. There is no particular place to identify yourself otherwise. If the people want to check, your DBA filing is public information specifically intended to let people know who they are doing business with. They can look up the business name in the county or state - however it works there in NJ.
You can't file a DBA in New Jersey, if you've registered your company previously in NJ. However, you can register "Fictitious / Alternate Name" (which is basically the same thing). You can then officially use it for financial (banking), and advertising purposes.
As of today, you can't file it online, but mail and fax (additional fees may apply) options only.