What is the ruling on reciting Al-Fatihah at the graveyard and a woman saying, "Al-Fatihah for the soul of the deceased," and what is the ruling on reciting the Qur'an or performing Salah on behalf of the deceased?

Scholars have differed concerning the ruling on reciting the Qur'an at graves. Some have preferred the permissibility of reciting Al-Fatiha and other surahs and dedicating their reward to the Muslim deceased, because the reward of an action belongs to its doer, and he may gift it to whomever he wishes, as long as the recipient is not a disbeliever. As for praying on behalf of the deceased, it is not valid, because it is a purely physical act of worship that does not accept proxy.