Korn is an Old High German word. It was used by the Saxons, earlier than Middle English.Pretty much, yes. A lot of Germanic and Scandinavian on top and more recently Hispanic and Caribbean influences, but in terms of both spelling and idiom, there's a great deal of 16th century English still there.
With regards to corn as a generic word for any cereal or grain-bearing crop, it goes back to Middle English meaning simply a grain, whether sand, salt or wheat. John Barleycorn was used as an euphemism for alcoholic beverages made from grain from the early 15th century.
It appears in old Runick rhyme.