Is it permissible to give money instead of food to the needy, or to give the amount to a charity, in fulfillment of a vow to feed a certain number of needy people with a specific amount of money?

One must fulfill a vow (nadhr) in the manner in which it was made by its owner. Therefore, the specified amount must be disbursed and converted into food to be distributed to the poor, unless cash would be more beneficial for the poor, in which case it is permissible to distribute it to them. One can delegate a trustworthy entity, such as a charity organization or reliable individuals, to distribute the vow, informing them that it is a vow intended for the poor.