Is expiation (kaffarah) obligatory for someone who made a vow (nadhr) while ignorant of the vow and its ruling, and does expiation multiply if the vows are multiple?

Your statement: "If something happens, I will pray two cycles (rak'ahs) to Allah every night" is not considered a vow (nadhr) as long as you did not intend it as a vow and were unaware of its implications. Therefore, you are not required to offer expiation for not performing this prayer. A vow is not binding on a minor. Fulfilling a vow carries reward and recompense, and Allah Almighty has praised those who fulfill their vows.