Is it permissible to dedicate the reward and merit of following a funeral procession, praying over the deceased, and attending the burial to a deceased father, and will it reach him?

It is permissible to dedicate the reward of acts of proximity (qurbat) to a Muslim, whether living or deceased. This includes dedicating the reward of the funeral prayer, following the bier, and attending the burial to one's father. The reward will reach him, by the permission of Allah.