The diagonal orientation of the DDR3 chip and corresponding diagonal traces I suspect is a choice made by the author to ease the layout process - it's more likely that is hand laid out to get traces of somewhat similar length with a minimum of fuss, followed by a length matching tool. A non-standard orientation can cause issues with pick-and-place machinery, which usually will handle 90 degrees fine, and _often_ 45 degrees fine, but (AFAIK) _rarely_ anything else, but that's not a problem for the author because he's assembling it himself. A diagonal IC also usually results in wasted space, which you can see in the empty areas of the resulting board. A 90 degree orientation may have allowed for a few more decoupling capacitor banks, but since his board works, who am I to sit here and judge?
This sounds like nonsense. Pick and place machines don't pick up components perfectly deterministically. There is always a tilt and an offset when you are picking the part up, which is why a computer vision system has to account for part orientation and the center of the part. The machine must compensate the error by moving and rotating the part accordingly.
I didn't use autorouter: I haven't found any reasonable working KiCad plugin for it, and didn't want to buy and commercial software for a hobby project.
(I am the author)