Is it permissible to give an ongoing charity (sadaqah jariyah) on behalf of the deceased, and does its reward reach them, and is the one who performs it recompensed for that, and is it permissible to include the living with the dead in the same charity, and is the one who performs it recompensed if he dedicates it solely to the deceased?

Perpetual charity (Sadaqah Jariyah) is an endowment (waqf), and its reward reaches the one for whom it is dedicated. So, if you dedicate the reward of charity to your father, he benefits from it. If you dedicate it for both of you, both of you benefit. And if you dedicate it for him, you receive the reward for your dutifulness to him. Allah does not let the reward of those who do good go to waste.