Sending an editor an outline like you describe won't have much of an effect. All an editor will do, if they respond at all, is say "why don't you submit the paper, and then we will decide whether to send it for peer review and to accept it". They couldn't possibly be any more committal based on just an email.

Writing mathematical papers is hard! Graduate students and early postdocs struggle a lot with that, and typically rely on considerable input from their advisors or other more senior colleagues to produce a paper that is submittable.

What I would recommend is that you first find a professional mathematician who is interested in your problem, and contact them with the questions that you would ask an editor. If you cannot find a mathematician who is interested in your problem, then that does not bode well for your journal submission (since if the editor cannot find anybody interested in it, they will reject the paper).