Since the rules text of Sphinx of New Prahv states that spells targeting it cost more to cast, shouldn't that also apply to spell counters which specifically say "Counter target spell?"
They do not. Creature abilities only work on the battlefield unless otherwise stated in the ability's text (Reassembling Skeleton references the graveyard, anything with cycling has to be in hand Irrigation Fields) so its ability will not function until it has resolved.
Compare Sphinx of New Prahv with Kaervek's Torch, which says "As long as Kaervek's Torch is on the stack..." (C.R. 108.1), so that the ability where that text appears functions only on the stack (C.R. 113.6b; see C.R. 113.6 for the general rule).
RULES OF MAGIC :
http://magic.wizards.com/en/game-info/gameplay/rules-and-formats/rules