Is it obligatory to fulfill a vow to pray two Rak'ahs of gratitude daily after learning of their unlawfulness, or is a prostration of gratitude sufficient, or is it not obligatory to fulfill the vow?

In Islamic law, there is no prayer called "two rak'ahs of gratitude" (ركعتي الشكر). Rather, there is the prostration of gratitude (سجود الشكر), which is recommended (mustahabb). Accordingly, vowing to perform "two rak'ahs of gratitude" is invalid and does not require fulfillment, because it is a vow for something not legislated. As for vowing to perform the prostration of gratitude upon receiving a blessing or repelling an affliction, it becomes obligatory to fulfill it when its cause arises.