So - even ignoring the colour and the point chosen for tesselation, which your first four points address, as you say this projection is bizarre as it has awful distortions (see the width of south vs North America and how the meridian lines are spaced), and the lack of navigability bought about by the twisted axis, and absence of north and south.
You want to show the globe accurately, you show a globe.
You want a better projection - turn Mercator on its side.
You want to show the globe accurately, you show a globe.
You want a better projection - turn Mercator on its side.