What is the ruling on the fasting and prayer of my sick grandmother who is unconscious and unable to speak, and are we obligated to make up for them on her behalf?

Whoever reaches a state of senility or delirium, and their mind changes, is exempt from fasting and prayer, and there is no expiation upon them. This is because a prerequisite for accountability (taklif) is a sound mind, as the Prophet, peace and blessings be upon him, said: "The pen has been lifted from three: from the sleeper until he awakens, from the child until he reaches puberty, and from the insane person until he regains his sanity." Some narrations add: "and from the senile."

As for someone who is aware and understands but left fasting due to illness: if their illness is expected to be cured and they have not recovered, then there is nothing upon them. However, if their illness is not expected to be cured, then it is obligatory to give expiation for each day by feeding a poor person (half a sa' of the staple food of the land). If it has not been given, then her family must give it now from her wealth.