Does a father's undertaking to support his son's pursuit of religious knowledge count as ongoing charity (Sadaqah Jariyah) for his deceased mother, and is it permissible for the son to request that from his father?

There is no objection to your father giving charity on behalf of your mother. Voluntary charity to a son is permissible, especially if it helps him in seeking religious knowledge. Giving money to a son is not considered an ongoing charity (Sadaqah Jariyah); an ongoing charity is an endowment (waqf). Giving money to students of knowledge without a continuous endowment is considered ordinary charity. See Fatwas no. 97296 and 119101 regarding the expenditure of an impoverished son on his well-off father.