A face-up plane card that's turned face down becomes a new object with no relation to its previous existence. In particular, it loses all counters it may have had.
Izzet Steam Maze
If the spell that's copied is modal (that is, it says "Choose one —" or the like), the copy will have the same mode. Its controller can't choose a different one.
If the spell that's copied has an X whose value was determined as it was cast (like Earthquake does), the copy has the same value of X.
Magic: The Gathering · ™ & © Wizards of the Coast · Illus. Franz Vohwinkel
Card data via Scryfall. Rarix is fan-made; not endorsed by the rights holders.
