Is it permissible to pray on behalf of the deceased who missed prayers due to illness, and is it permissible for me to make up the fasting on his behalf, or is that restricted to his guardian?

Illness is not an excuse to abandon prayer as long as one's mind is present. The sick person prays to the best of their ability. However, if the mind is absent, prayer and other acts of worship are lifted from them, as the Prophet, peace and blessings be upon him, said: "The pen is 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."

Therefore, if your relative abandoned prayer while being of sound mind, he erred. But if his mind was absent, then there is no make-up prayer due from him.

As for fasting, if the excuse persisted until his death, there is no make-up fasting or feeding due from him. However, if he was able to make up the fasts but did not, then it is permissible for his guardian to fast on his behalf or to feed a mudd (approximately 750 grams) of food for each day.