How to Make Wudu with a Cast
Question

How can a person fulfil his religious obligations of Wudu and prayer when his right arm is broken and is in a cast?
Praise be to Allah.How to make Wudu with a cast 
If a person is unable to move his right arm and use it when doing acts of worship, then he must be careful to adhere to the following Shar`i rulings:
Wudu and Ghusl are obligatory and are not waived because of his right arm being broken , because he can use his left arm to take water and make it reach the parts of the body that must be washed when purifying himself. He must be careful and deliberate when doing that to ensure that the act of purification is done properly.
With regard to the right arm which is broken and in a cast , it is sufficient, when doing Wudu and Ghusl, to wipe over it lightly so that the plaster will not be affected, and it can be wiped once only and does not have to be done repeatedly, unlike washing the arm [as is usually done]. Thus the act of purification will be sound, in sha Allah. It is also essential to note that the fingers or elbow of the right hand, if they are uncovered, must be washed; wiping is only acceptable with regard to the part that is hidden beneath the cast.
Shaykh Ibn `Uthaymin (may Allah have mercy on him) said:
“Sometimes the cast covers the palm and the fingers are not covered. In that case, it is obligatory to wash the fingers and the cast may be wiped over. Similarly, in the case of [a cast on] the leg , the toes may be not covered, so they must be washed and the cast must be wiped over.” (Al-Liqa’ Ash-Shahri, 61/27)
How to pray with a cast
With regard to prayer, the actions of the right arm may be summed up as follows:

Raising the arm when saying the four Takbirs (when commencing the prayer (Takbirat Al-ihram), when bowing, when standing up from bowing, and when rising from the first Tashahhud).
Placing the right hand over the left hand when standing.
Resting on the arm when prostrating.
Placing the hands on the thighs when sitting.
Pointing with the forefinger when reciting the Tashahhud.

In all of these cases, if you can move the arm that is in plaster and do these actions if possible, then that is better and is preferable. If you are not able to complete the full movement with your arm, then you should do as much as you are able. If you are not able to move it, then there is no blame on you, and you only have to move the left arm when doing these actions, with the exception of pointing with the forefinger, which should be done only with the right hand.
The Shar`i evidence for all of the above is two general juristic principles, for which are proven by many religious texts of the Quran and authentic Sunnah.

The first principle: Hardship dictates leniency. The evidence for which is the verse in which Allah, may He be exalted, says (interpretation of the meaning): “Allah does not burden any soul with more than it can bear” [Al-Baqarah 2:286]
The second principle: What one is able to do cannot be waived on the grounds of what one is unable to do. The evidence for which is the verse in which Allah, may He be exalted, says (interpretation of the meaning): “So fear Allah as much as you are able.” [At-Taghabun 64:16] This is an important principle concerning which the scholars say: “It is one of the basic principles that cannot be overlooked so long as the principles of Shari`ah are adhered to.” (Al-Ashbah wan-Nadha’ir by As-Suyuti, p. 293)

Shaykh Al-Islam Ibn Taymiyah (may Allah have mercy on him) said:
“There are many religious texts which indicate that the actions that are enjoined are subject to the condition that one be able to do them, as the Prophet (blessings and peace of Allah be upon him) said to `Imran ibn Husayn: “Pray standing; if you cannot, then sitting; and if you cannot then lying on your side.” (Narrated by Al-Bukhari, 1117)
The Muslims unanimously agreed that if a worshipper is unable to do some of the obligatory parts of the prayer – such as standing, sitting, bowing, prostrating, covering the `Awrah, facing the Qiblah, and so on – then what he is unable to do is waived in his case. Rather what he is obliged to do is that which, if he seriously wanted to do it, he could do it. 
It is important to note that the Shar`i definition of one’s ability to comply with the commands and prohibitions is not the ability to do so even if it leads to harm. In fact if a person is able to do something but it would harm him , then he is regarded as being like one who is unable to do it in many instances, such as purifying himself with water, fasting when he is ill, standing in the prayer, and so on, in accordance with the words of Allah, may He be exalted (interpretation of the meaning):
“Allah intends for you ease and does not intend for you hardship.” [Al-Baqarah 2:185]
“[Allah] has not placed upon you in the religion any difficulty.” [Al-Hajj 22:78]
“Allah does not intend to make difficulty for you.” [Al-Ma’idah 5:6]
In an authentic narration from Anas (may Allah be pleased with him), the Prophet (blessings and peace be upon him) said: “You have been sent to make things easy, and you have not been sent to make things difficult.” (Majmu` Al-Fatawa, 8/438-439)
And Allah knows best.