Is it permissible for a father to take food from the school cafeteria to meet his household needs due to financial hardship, knowing that he spends his own money on the school and poor students? And does this act render his supplications unacceptable?

Your father is not permitted to take food from the school cafeteria home without permission, because doing so constitutes a breach of trust and the unlawful consumption of others' property. He must be advised to cease this action. If he persists, it is not permissible for you to eat it. However, if what he takes is leftover food after the students have eaten, and it would otherwise spoil and be discarded, then there is no harm in him benefiting from it at that point.