Cipher rules text says that you cast a copy of the spell. Does the copy have cipher too?
It doesn't. Only the non-copy version of the spell has the cipher ability
702.98a Cipher appears on some instants and sorceries. It represents two static abilities, one that functions while the spell is on the stack and one that functions while the card with cipher is in the exile zone. "Cipher" means "If this spell is represented by a card, you may exile this card encoded on a creature you control" and "As long as this card is encoded on that creature, that creature has 'Whenever this creature deals combat damage to a player, you may copy this card and you may cast the copy without paying its mana cost.'"