According to the view of Shaykh al-Islam Ibn Taymiyyah, is the prayer valid and rewarded, or does it merely fulfill the obligation without reward, if its performer unknowingly violates a condition or a pillar?

The mentioned act of worship fulfills the obligation and absolves the doer from the need for a make-up (qada'). The doer is rewarded for it, because the Sheikh states that the doer of an invalid act of worship is rewarded for the remembrance and similar acts contained within it, even if it does not absolve them from the obligation. For jurists, invalidity means that a make-up is required, not that there is no reward for it in the Hereafter.