All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger as well as that of his family and all his companions.
There is no age limit by which a person is exempted from fasting and praying. However, an old man could be exempted from fasting in two cases.
1- If he is no longer held accountable because of loosing his consciousness due to senility and the like. In this case he does not have to fast and he does not have to expiate for this as he is no longer held accountable for his acts. The Prophet, sallallaahu alayhi wa sallam, said: "The pen is lifted (stopped from writing the deeds) from three kinds of people: a sleeping person until he wakes up, a mentally-handicapped or insane person till he can reason, and a child till he reaches the age of puberty." [An-Nasaa'ee]
2- If he is unable to fast due to his old age, then he is exempted from fasting and he has to expiate for it, which is to feed a poor person for every day he broke the fast.
As regards performing the prayer, a person is not exempted from it under any circumstances as long as a person is conscious. However, if a person fails to fulfil one of its conditions, or a pillar from its pillars, then he has to perform the prayer according to his ability.
Allaah Knows best.