These are all good observations, but they just follow on from PostScript, which is what the PDF is based on.
In 1987 I started working at a desktop publishing company and was assigned the job of rationalizing the printer drivers. I quickly discovered that while most laser printers had their origin at the top left corner, the Apple LaserWriter (a PostScript printer) had its origin at the bottom left corner. So for most printers, going down the page meant increasing y values, but for the LaserWriter it meant a decreasing y value.
As you describe, joining lines could be done by filling out a triangle (meaning lines meeting at a small angle left a big elbow), by chopping off the triangle (making lines meeting at 90 degrees have a 45 degree corner) or by having a rounded corner. PostScript is very flexible that way, but can also be quite CPU-intensive.
Adobe's Red Book and Blue Book were my PostScript bibles back then.