> Would it be unethical to put my own pieces in an issue once in a while?
IMO, the sacred duty of editing is to spend your readers’ attention well. If you genuinely believe that, if written by a stranger, those pieces would have passed editorial muster, then I don’t think it’s unethical. At worst, it’s on a spectrum with soliciting friends.
> Would it affect my and the magazine’s reputation and integrity?
Self-publishing tends to lower my opinion of a press, yes. I don’t consider it an integrity violation if done above board.