Νίκος said:
Rameses II completed the MO too and he concously chose to die and be reborn to do Satan's work at a later date. Who's to say Alexander didn't do the same? Genghis also asked a Taoist monk to teach him the MO. He probably finished and then hit reset too.
Genghis and Alexander lived relatively identical lives with relatively identical mentalities. Both were redheads who have a very different biochemistry and nerves system from other hair cholors which implies that redheads will reincarnate as redheads due to a distinct soul type. They're too similar to discount.
Plus, if a conqueror becomes a god and allows his kingdom to fall and his world to become the worst shithole imaginable while he's still here, he clearly isn't doing his job. So I can only assume Alexander hit the reset button like Rameses did
Ramses II didn't completed the Magnum Opus.Further proof for that can be the fact that figure of the past needed some decades of advancement to complete the MO.
Also soul's don't reincarnate in other race's.Alexander was Mediterranean White and Genghis was Asian (even if he is half Asian or not Asian genes are more dominant than white genes).So there is no point on doing so.Regarding the appearance from what I know there are not much info about Genghis' personal life or appearance.Someone named Rasid al-Din has claimed his appearance is like you described but he hasn't met him in person so I don't think this is a trustworthy source.
Now regarding Alexander there is only one coloured picture woth him ever found and from it he seems to have browm hair something totally normal for a greek person.
Now regarding the last part of your post there is no historical source that Alexander's empire was problematic before his "death"(which from my opinion was tye time he completed magnum opus and left the earth).