He cannot control his urine and he is very old; should he fast and pray?

The ruling concerning your father differs depending on his
state of mind. If he loses his reason and his memory then he should not be
told to purify himself or to pray or fast, but when his mind is present and
focused and his memory is with him, then he should be told to do the duties
enjoined by sharee’ah as best as he can, without causing himself undue
hardship. 

Shaykh Muhammad ibn Saalih al-‘Uthaymeen (may Allaah have
mercy on him) was asked: 

Do those who have lost their memory, the feeble-minded, young
children and the insane have to fast? 

He replied: 

Allaah has enjoined acts of worship on man if he is able to
bear that obligation, by being of sound mind and able to understand things.
But if he is not of sound mind then he does not have to do those acts of
worship. So the insane and young children who have no powers of discernment
do not have to do these acts of worship. This is by the mercy of Allaah, may
He be glorified and exalted. The same applies to the feeble-minded person
whose mind is affected in some way but not to the degree of insanity and the
elderly person who has lost his memory, as this questioner says, do not have
to fast, pray or purify themselves, because the one who has lost his memory
is like a small child who has no power of discernment, so the duties of
Islam are waived for him and he does not have to purify himself or pray, nor
does he have to fast. With regard to the financial obligations, they are
required of his wealth even in this case, so zakaah – for example – must be
paid by his guardian on his wealth if it reaches the amount at which zakaah
becomes due, because the obligation of zakaah is connected to wealth, as
Allaah says (interpretation of the meaning): 

“Take Sadaqah (alms) from their wealth in order to purify
them and sanctify them with it, and invoke Allaah for them. Verily, your
invocations are a source of security for them; and Allaah is All-Hearer,
All-Knower”

[al-Tawbah 9:103]

He did not say “take it from them.” 

And the Prophet (peace and blessings of Allaah be upon
him) said to Mu’aadh (may Allaah be pleased with him) when he sent him to
Yemen: “Teach them that Allaah has enjoined on them sadaqah (charity) from
their wealth, to be taken from their rich and given to their poor.” He said,
“Charity from their wealth” and explained that it is to be taken from their
wealth, even though it is to be taken from the owner of the wealth.  

Whatever the case, the
financial obligations are not waived for a person in this case, but the
religious obligations such as prayer, purification and fasting, are waived
in the case of people like this man, because he does not have any powers of
understanding. 

Majmoo’ Fataawa al-Shaykh Ibn ‘Uthaymeen,
10, question no. 40. 

The Shaykh (may Allaah have mercy on him) was also asked: 

What is the ruling on fasting for one who is sane sometimes
and insane at other times, or who is incoherent one day and focused another
day? 

He replied: 

The ruling changes according to the reason. At times when he
is conscious and aware, he has to fast, and at times when he is insane and
incoherent, he does not have to fast. If we assume that he is insane one day
and sane another, or incoherent one day and focused another, then on the
days when he is focused he has to fast, and on the days when he is
incoherent he does not have to fast. 

Majmoo’ Fataawa al-Shaykh Ibn ‘Uthaymeen,
10, question no. 43. 

And Allaah knows best.