Is it permissible to give a portion of Zakat al-Mal to needy relatives for whom we are not obligated to provide, and is it permissible to give an ongoing charity (Sadaqah Jariyah) on behalf of the deceased from Zakat money?

If a relative is eligible to receive zakat, then giving it to them is more meritorious, based on the Prophet's (peace be upon him) saying: "Charity given to a poor person is one charity, but to a relative, it is two: charity and maintaining kinship ties."

Performing ongoing charity (sadaqah jariyah) on behalf of your father is a good deed, and you will be rewarded for it. However, it is not permissible to use zakat funds for ongoing charity, because zakat funds cannot be endowed. Rather, it is necessary for the eligible recipients to take ownership of them. Zakat has specific categories of recipients, and it is not permissible to disburse it for purposes other than these.

Therefore, disburse the zakat to its designated recipients as determined by Allah Almighty. Then, if you wish to dedicate the reward of ongoing charity to your father from funds other than zakat, do so, and you will be rewarded.