Good point. If the OP owns a gun, chances are he has a license for it.
Depends where the OP lives. Not every jurisdiction requires a license / permit / FOID card to buy a gun. There's no government record of me purchasing ANY firearms (unless someone is illegally keeping records of the NCIS check, which I doubt happens here). If CPB asked me that question, I'd laugh it off.
I would guess the CPB agent was fishing, or looking for nervousness that could indicate the OP's brother was trying to get into the US on the OP's papers.