Monarchy is not necessary hereditary. And replacing monarch with sovereign, doesn't change the fact that it's a monarchy.
I guess the only real definition of monarch is social and cultural: someone who claims to be one and is broadly recognized as such.
Not really. Reza Khan was just a colonel in the army before the coup that later established him as Shah of Iran. Osman of the Ottoman Empire and his descendants for a very long time had no aristocracy or nobility to speak of, only temporary (land reverted to the Sultan at death) land owners.