Can a cipher copy be countered by a counter spell? Or, since the card has been encoded to a creature, does it act more like an ability, and can only be countered by cards like Stifle and others like it?
A spell created by a cipher is a regular spell, except that there is no physical card on the stack. You can counter it like you would counter the original. As the ability says:
Whenever that creature deals combat damage to a player, its controller may cast a copy of this card without paying its mana cost.
All rules applying to spells also apply to copies of spells, for copies of spells are spells.
111.1a A copy of a spell is also a spell, even if it has no card associated with it.