What is the ruling on and origin of reciting "La ilaha illallah" (There is no god but Allah) seventy thousand times, and does its reward reach the deceased, and are the family of the deceased required to do so?

"There is no god but Allah" is among the best forms of remembrance (dhikr). However, reciting it a specific number of times to free the deceased from Hellfire is an added innovation (bid'ah idafiyyah) that is impermissible and will not benefit the deceased. Rather, the one who does it incurs sin. Similarly, it is not permissible for the family of the deceased to hold banquets and mourning gatherings, as these contravene the Sunnah.