A fighter that takes the archetype spear fighter uses the feats Power Attack, Furious Focus, and Improved Furious Focus. If he uses parry and riposte, does he incur the penalties from having used Power Attack?
Yes, the Power Attack penalty to attack rolls is applied when using the Spear Fighter’s Spear Parry ability.
This is because the parry is an attack of opportunity - as outlined in the quotes below - which does not benefit from Improved Furious Focus, as the feat explicitly calls them out as not affected.
At 3rd level, a spear fighter learns to parry his opponents’ attacks with his spear. This functions as a swashbuckler’s opportune parry and riposte deed....
Opportune Parry and Riposte:
...when an opponent makes a melee attack against the swashbuckler, she can spend 1 panache point and expend a use of an attack of opportunity to attempt to parry that attack. The swashbuckler makes an attack roll as if she were making an attack of opportunity....
Improved Furious Focus:
When you are wielding a two-handed weapon or a one-handed weapon in two hands and using the Power Attack feat, you do not suffer Power Attack’s penalty on attack rolls on your turn. You still suffer the penalty on attacks of opportunity.
(Keep in mind you also still have the penalty when taking attacks of opportunity during your own turn)