“S” = South, it cannot be in Northern hemisphere. You are probably confusing it with MGRS latitude bands, but they are not a part of UTM specification.

It is only by agreement. The fact that the zones do not overlap is purely by agreement, and not by math limitations or distortion-aware considerations. If interpreted as a new equator, the zone centre meridian define a “stripe” on Earth’s surface of constant width of 668 km (from -3º to +3º), but they are artificially reduced, because we cannot forget that we came from WGS84. Mathematically nothing is stopping us from using the projection in any area on the planet. The projection will work just fine and will maintain the same level of distortions at any location within the “stripe”. But what happens in this case? The regions closer to WGS84 poles will face more and more overlap, projecting the same areas within different adjacent “stripes”. The overlaps will look as rotated versions of adjacent projections, with pole areas going to extreme: they would have 60 projections of the same 668 km “circle”, just with different degree of rotation. Such overlaps would be confusing for a system designed to be XY-intuitive in mind, so they do two things: 1) they design zone borders to not overlap (mostly following WGS84 meridians), 2) they limit upper and lower latitudes by artificial 84⁰N and 80⁰S thresholds (subject to cartography need in those regions).

That’s an interesting idea! Reducing the zone width from 6° to 5.99678° would slightly decrease distortion near the edges since transverse Mercator projections distort more with distance from the central meridian. While the improvement would be small (since 0.00322° is approximately 350 meters at the equator), fine-tuning zone boundaries could be useful in high-precision applications.

In practice, most systems (like UTM) manage distortion using a scale factor (e.g., 0.9996) or overlapping zones, but your suggestion could be explored further for specialized mapping needs. Thank you for sharing this perspective; it’s a great insight into how minor adjustments can impact projection accuracy.

Because the distance between two parallel and meridian is not constant value on pole. Besides this, the shape of the earth become flatten on the pole. This why cylindrical projection is not applicable for polar regions.

Those look like decimal degree coordinates (lat/long). Here’s more information on DMS and DD – Degrees/Minutes/Seconds (DMS) vs Decimal Degrees (DD)