Q1: The arXiv moderation procedure is described here; as you can read, "unrefereeable content" is a placeholder for a paper "in need of significant review and revision". Unlike refereeing, which has a relaxed time schedule, moderation is done in the 6 hour time frame between the closure of the submission window and the announcement of the new submissions. A typical moderator may find themselves deciding on a dozen submissions, so this is very much a rapid decision, and first impressions can make a big difference. A submission from a personal rather than institutional email address, formatted in a somewhat unusual way, with minimal references to the literature, on a topic where everyone and their dog seems to have an opinion, may very well trigger an unjustified negative decision.
Q2: The mathematics moderators are listed here, but it is considered inappropriate to contact a moderator directly. The appeals process, described here, outlines the steps to take, and also points out that it may be a lengthy process.
Q3: It is worth to appeal, because that will allow the moderators to take the time they would not have in their ordinary work flow. A careful look at your note should convince them this is substantial research.