First of all, the question is a small matter that only a journal editor should take seriously. There are much deeper reasons that a paper might be well written or poorly written. Even among the concerns at this level, it is more important to use concise, regular, correct grammar than to follow particular journal conventions.
That said, in my opinion it's okay to say "above" and "below" to refer either to an equation, or more often to a paragraph of the paper. E.g., you might say "By the above discussion...". But it may be clearer to do something else for equations. If you just say "above", it may not be clear if it means immediately above (or previous) or something else; but if you say "immediately above", that's a bit strained. My rule is to say "this" equation if it is immediately previous, and otherwise to number the equation even if I only explicitly cite it once. If the equation is not explicitly cited, but is just part of the narrative, then like you I wouldn't number it. But there are authors who number every equation.
For paragraphs, I sometimes say "above" and "below", if the cited paragraph is in the same section and subsection.